Adding exponents - Easy but its teasing my brain

Question

Hi everyone-

What is the rule in solving this problem:

2 + 2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

a)2^9
b)2 ^10
c) 2^16
d) 2^35
e)2^37

I believe there is a quick way to do this but I can't figure it out.
Thanks

zonk · Answer

Are you sure this question is correct?

2 + 2^2 + 2^3 + ... + 2^8 = 510
2^9 = 512

bhushangiri · Answer

The question as is also looks correct. Take 2+2 as 4 or 2^2. This becomes a geometric series with first term 2^2 and ratio=2

maratikus · Answer

It probably was 2^2+2^2+2^3 + ...

the rule is very simple 2^k+2^k = 2*2^k = 2^(k+1)

2^2+2^2 = 2^3, then 2^3+2^3 = 2^4, ... , 2^8+2^8 = 2^9

zonk · Answer

This makes much more sense.

abhishekv · Answer

Hey..

i guess u r all complicating things here..

its is like
2^(1+1+3+4+5+6+7+8) = 2^35

rishi2377 · Answer

take the short form of the series.
=> 2 + 2 + 2^2 + 2^3
=> 2(1 + 1 + 2 + 2^2)
=> 2(2 + 2 + 2^2)
=> 2x2 (1 + 1 + 2)
=> 2x2x2 ( 1+1)
=> 2^3 (2) = 2^4

Through same mechanism given sequence will end in 2^8 (2) = 2^9

abhishekv · Answer

oopss..my reply ws incorrect...sorry guys

Prep Toolkit