What happens when you start to add up powers of 2, starting with 1

What happens when you start to add up powers of 2, starting with 1 Class 6

Question 1.

What happens when you start to add up powers of 2 starting with 1, i.e., take 1, 1 + 2, 1 + 2 + 4, 1 + 2 + 4 + 8, …? Now add 1 to each of these numbers — what numbers do you get? Why does this happen? Class 6

Solution:

We get 2, 4, 8, 16, and so on. These are powers of 2. On adding 1, the first term becomes 2, and in other terms, the sum of all the numbers (except the last number) becomes equal to the last number.