pattern

ST wrote:2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =

1) 2^9
2) 2^10
3) 2^16
4) 2^35
5) 2^37

answer is 1
anyone know why answer is not 5?

Here's another way to look at it.
Please note that 2^7 is half as large as 2^8 and, in general, 2^n is half as large as 2^(n+1)

Let's say that I have a lot of gold. I have 2^9 kg.
Today I give you half of all my gold. In other words, I give you 2^8 (which leaves me with 2^8 kg).
Tomorrow I give you half of my remaining gold. I give you 2^7 (which leaves me with 2^7 kg).
Each day I give you half of my remaining gold.
When I get to the eighth day, I give you 2 kg of gold (which leaves me with 2 kg)
Then, on the last day, I give you my last 2 kg of gold.
I have now given you all of my gold (all 2^9 kg)
So, we can see that 2^8 + 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2 + 2 + 2^9