What is the sum of the 20th row of pascals triangle?

Answer 1

Let's calculate the sums of few first rows of Pascal's triangle:

1st row: 1 = 1

2nd row: 1 + 1 = 2

3rd row: 1 + 2 + 1 = 4

Looks promising, let's continue:

4th row: 1 + 3 + 3 + 1 = 8

5th row: 1 + 4 + 6 + 4 + 1 = 16

We can make an assumption that each row's sum is twice the sum of previous row - it's a power of two.

But why is that?

If you know how Pascal's triangle is constructed, you should notice that when creating new row, you use the previous row numbers(except ones) two times in addition.

Considering ones, you only use each 1 in previous row once, but in the new row you always add two 1's on the sides.

Alternatively, you may think of empty space around Pascal's triangle as zeros and then you'll definitely use each previous row's numbers two times to create a new row.

The formula will be then:

s = 2n-1, where

s - sum of the nth row(we assume numeration starts with 1 for the single '1' on the top)

n - number of the row

Answer 2

The sum of the 20th row in Pascal's triangle is 1048576.

Answer 3

28354132 is the correct answer, I believe.