Posted on by Kalkicode
Code Mathematics

Find the sum of nth row in pascal's triangle

The sum of the numbers in the nth row of Pascal's triangle is equal to 2^n.

Pascal's triangle is a triangular array of numbers where each number in the triangle is the sum of the two numbers directly above it. The first row contains only the number 1, and each subsequent row is constructed by adding a 1 at the beginning and end of the previous row.

For example, the first few rows of Pascal's triangle look like this:

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1

To find the sum of the numbers in the nth row, you simply add up all the numbers in that row. For example, the sum of the numbers in the 5th row is:

1 + 4 + 6 + 4 + 1 = 16

The formula for the sum of the numbers in the nth row is 2^n. So, in this case, 2^5 = 32, which is twice the sum of the numbers in the 5th row. This formula holds true for all rows of Pascal's triangle.

/*
C program for
Find the sum of nth row in pascal's triangle
*/
#include <stdio.h>

// Sum of given row in pascal triangle
void sumPascalRow(int n)
{
if (n <= 0)
{
return;
}
printf("\n Row %d \n", n);
// Assume number is not overflow
long long int sum = (1 << n);
printf(" Sum : %lld \n", sum);
}
int main(int argc, char
const *argv[])
{
/*

1                 0-th row
1   1               1-st row
1   2   1             2-nd row
1   3   3   1           3-th row
1   4   6   4   1         4-th row
1   5   10   10   5   1     5-th row
1   6   15   20   15   6   1  6-th row
-----------------------------------------
Pascal's triangle
*/
/*
Example A

Row = 5th
[ 1  5   10  10  5   1 ]
-------------------------
[ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
*/
sumPascalRow(5);
/*
Example B

Row = 2nd
[ 1   2   1 ]
-------------------------
[ 1 + 2 + 1 ] = 4
*/
sumPascalRow(2);
/*
Example C

Row = 7th
[ 1  7  21  35  35  21  7  1]
------------------------------------------
[ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
*/
sumPascalRow(7);
return 0;
}

Output

Row 5
Sum : 32

Row 2
Sum : 4

Row 7
Sum : 128
// Java program for
// Find the sum of nth row in pascal's triangle
public class PascalTriangle
{
// Sum of given row in pascal triangle
public void sumPascalRow(int n)
{
if (n <= 0)
{
return;
}
System.out.print("\n Row " + n + " \n");
// Assume number is not overflow
long sum = (1 << n);
System.out.print(" Sum : " + sum + " \n");
}
public static void main(String[] args)
{
/*

1                 0-th row
1   1               1-st row
1   2   1             2-nd row
1   3   3   1           3-th row
1   4   6   4   1         4-th row
1   5   10   10   5   1     5-th row
1   6   15   20   15   6   1   6-th row
---------------------------------------
Pascal's triangle
*/
/*
Example A

Row = 5th
[ 1  5   10  10  5   1 ]
-------------------------
[ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
*/
/*
Example B

Row = 2nd
[ 1   2   1 ]
-------------------------
[ 1 + 2 + 1 ] = 4
*/
/*
Example C

Row = 7th
[ 1  7  21  35  35  21  7  1]
------------------------------------------
[ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
*/
}
}

Output

Row 5
Sum : 32

Row 2
Sum : 4

Row 7
Sum : 128
#include <iostream>

using namespace std;
// C++ program for
// Find the sum of nth row in pascal's triangle
class PascalTriangle
{
public:
// Sum of given row in pascal triangle
void sumPascalRow(int n)
{
if (n <= 0)
{
return;
}
cout << "\n Row " << n << " \n";
// Assume number is not overflow
long sum = (1 << n);
cout << " Sum : " << sum << " \n";
}
};
int main()
{
/*
1                 0-th row
1   1               1-st row
1   2   1             2-nd row
1   3   3   1           3-th row
1   4   6   4   1         4-th row
1   5   10   10   5   1     5-th row
1   6   15   20   15   6   1   6-th row
---------------------------------------
Pascal's triangle
*/
/*
Example A
Row = 5th
[ 1  5   10  10  5   1 ]
-------------------------
[ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
*/
/*
Example B
Row = 2nd
[ 1   2   1 ]
-------------------------
[ 1 + 2 + 1 ] = 4
*/
/*
Example C
Row = 7th
[ 1  7  21  35  35  21  7  1]
------------------------------------------
[ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
*/
return 0;
}

Output

Row 5
Sum : 32

Row 2
Sum : 4

Row 7
Sum : 128
// Include namespace system
using System;
// Csharp program for
// Find the sum of nth row in pascal's triangle
public class PascalTriangle
{
// Sum of given row in pascal triangle
public void sumPascalRow(int n)
{
if (n <= 0)
{
return;
}
Console.Write("\n Row " + n + " \n");
// Assume number is not overflow
long sum = (1 << n);
Console.Write(" Sum : " + sum + " \n");
}
public static void Main(String[] args)
{
/*
1                 0-th row
1   1               1-st row
1   2   1             2-nd row
1   3   3   1           3-th row
1   4   6   4   1         4-th row
1   5   10   10   5   1     5-th row
1   6   15   20   15   6   1   6-th row
---------------------------------------
Pascal's triangle
*/
/*
Example A
Row = 5th
[ 1  5   10  10  5   1 ]
-------------------------
[ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
*/
/*
Example B
Row = 2nd
[ 1   2   1 ]
-------------------------
[ 1 + 2 + 1 ] = 4
*/
/*
Example C
Row = 7th
[ 1  7  21  35  35  21  7  1]
------------------------------------------
[ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
*/
}
}

Output

Row 5
Sum : 32

Row 2
Sum : 4

Row 7
Sum : 128
package main
import "fmt"
// Go program for
// Find the sum of nth row in pascal's triangle
type PascalTriangle struct {}
func getPascalTriangle() * PascalTriangle {
var me *PascalTriangle = &PascalTriangle {}
return me
}
// Sum of given row in pascal triangle
func(this PascalTriangle) sumPascalRow(n int) {
if n <= 0 {
return
}
fmt.Print("\n Row ", n, " \n")
// Assume number is not overflow
var sum int64 = (1 << n)
fmt.Print(" Sum : ", sum, " \n")
}
func main() {
var task * PascalTriangle = getPascalTriangle()
/*
1                 0-th row
1   1               1-st row
1   2   1             2-nd row
1   3   3   1           3-th row
1   4   6   4   1         4-th row
1   5   10   10   5   1     5-th row
1   6   15   20   15   6   1   6-th row
---------------------------------------
Pascal's triangle
*/
/*
Example A
Row = 5th
[ 1  5   10  10  5   1 ]
-------------------------
[ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
*/
/*
Example B
Row = 2nd
[ 1   2   1 ]
-------------------------
[ 1 + 2 + 1 ] = 4
*/
/*
Example C
Row = 7th
[ 1  7  21  35  35  21  7  1]
------------------------------------------
[ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
*/
}

Output

Row 5
Sum : 32

Row 2
Sum : 4

Row 7
Sum : 128
<?php
// Php program for
// Find the sum of nth row in pascal's triangle
class PascalTriangle
{
// Sum of given row in pascal triangle
public	function sumPascalRow(\$n)
{
if (\$n <= 0)
{
return;
}
echo("\n Row ".\$n." \n");
// Assume number is not overflow
\$sum = (1 << \$n);
echo(" Sum : ".\$sum." \n");
}
}

function main()
{
/*
1                 0-th row
1   1               1-st row
1   2   1             2-nd row
1   3   3   1           3-th row
1   4   6   4   1         4-th row
1   5   10   10   5   1     5-th row
1   6   15   20   15   6   1   6-th row
---------------------------------------
Pascal's triangle
*/
/*
Example A
Row = 5th
[ 1  5   10  10  5   1 ]
-------------------------
[ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
*/
/*
Example B
Row = 2nd
[ 1   2   1 ]
-------------------------
[ 1 + 2 + 1 ] = 4
*/
/*
Example C
Row = 7th
[ 1  7  21  35  35  21  7  1]
------------------------------------------
[ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
*/
}
main();

Output

Row 5
Sum : 32

Row 2
Sum : 4

Row 7
Sum : 128
// Node JS program for
// Find the sum of nth row in pascal's triangle
class PascalTriangle
{
// Sum of given row in pascal triangle
sumPascalRow(n)
{
if (n <= 0)
{
return;
}
process.stdout.write("\n Row " + n + " \n");
// Assume number is not overflow
var sum = (1 << n);
process.stdout.write(" Sum : " + sum + " \n");
}
}

function main()
{
/*
1                 0-th row
1   1               1-st row
1   2   1             2-nd row
1   3   3   1           3-th row
1   4   6   4   1         4-th row
1   5   10   10   5   1     5-th row
1   6   15   20   15   6   1   6-th row
---------------------------------------
Pascal's triangle
*/
/*
Example A
Row = 5th
[ 1  5   10  10  5   1 ]
-------------------------
[ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
*/
/*
Example B
Row = 2nd
[ 1   2   1 ]
-------------------------
[ 1 + 2 + 1 ] = 4
*/
/*
Example C
Row = 7th
[ 1  7  21  35  35  21  7  1]
------------------------------------------
[ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
*/
}
main();

Output

Row 5
Sum : 32

Row 2
Sum : 4

Row 7
Sum : 128
#  Python 3 program for
#  Find the sum of nth row in pascal's triangle
class PascalTriangle :
#  Sum of given row in pascal triangle
def sumPascalRow(self, n) :
if (n <= 0) :
return

print("\n Row ", n ," ")
#  Assume number is not overflow
sum = (1 << n)
print(" Sum : ", sum ," ")

def main() :
#               1                 0-th row
#             1   1               1-st row
#           1   2   1             2-nd row
#         1   3   3   1           3-th row
#       1   4   6   4   1         4-th row
#     1   5   10   10   5   1     5-th row
#  1   6   15   20   15   6   1   6-th row
#  ---------------------------------------
#        Pascal's triangle
#    Example A
#    Row = 5th
#    [ 1  5   10  10  5   1 ]
#    -------------------------
#    [ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
#    Example B
#    Row = 2nd
#    [ 1   2   1 ]
#    -------------------------
#    [ 1 + 2 + 1 ] = 4
#    Example C
#    Row = 7th
#    [ 1  7  21  35  35  21  7  1]
#    ------------------------------------------
#    [ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128

if __name__ == "__main__": main()

Output

Row  5
Sum :  32

Row  2
Sum :  4

Row  7
Sum :  128
#  Ruby program for
#  Find the sum of nth row in pascal's triangle
class PascalTriangle
#  Sum of given row in pascal triangle
def sumPascalRow(n)
if (n <= 0)
return
end

print("\n Row ", n ," \n")
#  Assume number is not overflow
sum = (1 << n)
print(" Sum : ", sum ," \n")
end

end

def main()
#               1                 0-th row
#             1   1               1-st row
#           1   2   1             2-nd row
#         1   3   3   1           3-th row
#       1   4   6   4   1         4-th row
#     1   5   10   10   5   1     5-th row
#  1   6   15   20   15   6   1   6-th row
#  ---------------------------------------
#        Pascal's triangle
#    Example A
#    Row = 5th
#    [ 1  5   10  10  5   1 ]
#    -------------------------
#    [ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
#    Example B
#    Row = 2nd
#    [ 1   2   1 ]
#    -------------------------
#    [ 1 + 2 + 1 ] = 4
#    Example C
#    Row = 7th
#    [ 1  7  21  35  35  21  7  1]
#    ------------------------------------------
#    [ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
end

main()

Output

Row 5
Sum : 32

Row 2
Sum : 4

Row 7
Sum : 128
// Scala program for
// Find the sum of nth row in pascal's triangle
class PascalTriangle()
{
// Sum of given row in pascal triangle
def sumPascalRow(n: Int): Unit = {
if (n <= 0)
{
return;
}
print("\n Row " + n + " \n");
// Assume number is not overflow
var sum: Long = (1 << n);
print(" Sum : " + sum + " \n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: PascalTriangle = new PascalTriangle();
/*
1                 0-th row
1   1               1-st row
1   2   1             2-nd row
1   3   3   1           3-th row
1   4   6   4   1         4-th row
1   5   10   10   5   1     5-th row
1   6   15   20   15   6   1   6-th row
---------------------------------------
Pascal's triangle
*/
/*
Example A
Row = 5th
[ 1  5   10  10  5   1 ]
-------------------------
[ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
*/
/*
Example B
Row = 2nd
[ 1   2   1 ]
-------------------------
[ 1 + 2 + 1 ] = 4
*/
/*
Example C
Row = 7th
[ 1  7  21  35  35  21  7  1]
------------------------------------------
[ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
*/
}
}

Output

Row 5
Sum : 32

Row 2
Sum : 4

Row 7
Sum : 128
// Swift 4 program for
// Find the sum of nth row in pascal's triangle
class PascalTriangle
{
// Sum of given row in pascal triangle
func sumPascalRow(_ n: Int)
{
if (n <= 0)
{
return;
}
print("\n Row ", n ," ");
// Assume number is not overflow
let sum: Int = (1 << n);
print(" Sum : ", sum ," ");
}
}
func main()
{
/*
1                 0-th row
1   1               1-st row
1   2   1             2-nd row
1   3   3   1           3-th row
1   4   6   4   1         4-th row
1   5   10   10   5   1     5-th row
1   6   15   20   15   6   1   6-th row
---------------------------------------
Pascal's triangle
*/
/*
Example A
Row = 5th
[ 1  5   10  10  5   1 ]
-------------------------
[ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
*/
/*
Example B
Row = 2nd
[ 1   2   1 ]
-------------------------
[ 1 + 2 + 1 ] = 4
*/
/*
Example C
Row = 7th
[ 1  7  21  35  35  21  7  1]
------------------------------------------
[ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
*/
}
main();

Output

Row  5
Sum :  32

Row  2
Sum :  4

Row  7
Sum :  128
// Kotlin program for
// Find the sum of nth row in pascal's triangle
class PascalTriangle
{
// Sum of given row in pascal triangle
fun sumPascalRow(n: Int): Unit
{
if (n <= 0)
{
return;
}
print("\n Row " + n + " \n");
// Assume number is not overflow
val sum = (1 shl n);
print(" Sum : " + sum + " \n");
}
}
fun main(args: Array < String > ): Unit
{
/*
1                 0-th row
1   1               1-st row
1   2   1             2-nd row
1   3   3   1           3-th row
1   4   6   4   1         4-th row
1   5   10   10   5   1     5-th row
1   6   15   20   15   6   1   6-th row
---------------------------------------
Pascal's triangle
*/
/*
Example A
Row = 5th
[ 1  5   10  10  5   1 ]
-------------------------
[ 1 + 5 + 10 + 10 + 5 + 1 ] = 32
*/
/*
Example B
Row = 2nd
[ 1   2   1 ]
-------------------------
[ 1 + 2 + 1 ] = 4
*/
/*
Example C
Row = 7th
[ 1  7  21  35  35  21  7  1]
------------------------------------------
[ 1 + 7 + 21 + 35 + 35 + 21 + 7 + 1] = 128
*/
}

Row 5
Sum : 32

Row 2
Sum : 4

Row 7
Sum : 128

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