Question

Write an expression to represent the sum of the numbers in the nth row of Pascal’s triangle.

a.
n/2
c.
2n
b.
n²
d.
2n


Please select the best answer from the choices provided

A
B
C
D

Answer 1

Answer: The answer is 2^n, which could be c or d, depending on which lost the ^ in transcription.

Explanation:

Row 1 is 0 1 1 0, sum 2^1

Row 2 is 0 0+1 1+1 1+0 0 sum 2^2

Row 3 is 0 0+1 1+2 2+1 1+0 0 sum 2^3

Notice that every number on row n is used as a term twice in row n+1. So the sum doubles.

Answer 2

Choose from your options option where is given
`2^n`

Explanation:

Pascal's triangle is a number triangle with numbers arranged in staggered rows such that each n-th row consists of n+1 binomial coefficients.

The sum of the numbers in the n-th row of Pascal’s triangle is

`C^n_0+C^n_1+C^n_2+C^n_3+\dots +C^n_(n-2)+C^n_(n-1)+C^n_n.`

This sum for every n is always equal to
`2^n.`