1+2+2^2+2^3+2^4+2^5=？

[Max@Math Revolution]

1+2+2^2+2^3+2^4+2^5=？
A. (2^3-1)(2^3+1)
B. 2^6+1
C. 2^5-1
D. 2^5+1
E. 2^5-2

*An answer will be posted in 2 days

[Max@Math Revolution]

From 1+2+2^2+2^3+2^4+2^5=1(2^6-1)/(2-1)=2^6-1=(2^3-1)(2^3+1), the correct answer is A.

[danielle07]

The answer would be

A. (2^3-1)(2^3+1)

[Matt@VeritasPrep]

Here's a little hocus pocus:

63 =>

2� - 1 =>

(2� + 2¹ + 2² + 2³ + 2� + 2�) * (2 - 1) =>

2� + 2¹ + 2² + 2³ + 2� + 2�

[Matt@VeritasPrep]

The way to solve this under test conditions, however, is to look for a pattern.

1 + 2 = 3 = 2*2 - 1

1 + 2 + 4 = 7 = 2*2*2 - 1

1 + 2 + 4 + 8 = 15 = 2*2*2*2 - 1

Aha! If I add the first n nonnegative powers of 2 on the left, I come out with 2� - 1 on the right. Under test conditions, I'll just assume that this is true and roll with it, without bothering to discover why (and on the GMAT, this will work out for me most of the time).