Adding exponents

Question

I'm sure this question has been asked, but it's hard to search for:

2^1 +2^1 +2^2+ 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =

I'm having trouble factoring it out.

Thank you!

Aleehsgonji · Answer

2^1 +2^1 +2^2+ 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8

2^1 +2^1 = 2*2^1 = 2^2
2^2 + 2^2 = 2*2^2 = 2^3

So 2^1 +2^1 +2^2 form 2^3
Similarly 2^1 +2^1 +2^2+ 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 is equal to 2^9

nplaneta · Answer

nss123 · Answer

Excellent, thank you!

jullysabat · Answer

Very Nice Explanation..
U have made it so very precise and clear..

Kissa · Answer

Thanks a lot. It. Looks so easy now!

runitback · Answer

Alternate solution (not really practical here but maybe in a similar problem?):

2^1 +2^1 +2^2+ 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 = ?

Represented in binary:

0000000010 +
0000000010 +
0000000100 +
0000001000 +
0000010000 +
0000100000 +
0001000000 +
0010000000 +
0100000000 =
----------------
1000000000

I've just started my GMAT prep recently so feel free to disregard if this doesn't sound helpful, but changing bases can be helpful sometimes =]

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