I think one might consider another "GRE-approach" here. that is trying to estimate the answer w/o actually solving the problem. this approach is described thoroughly in MIT course "Street-Fighting Mathematics" (available online here:
http://ocw.mit.edu/OcwWeb/Mathematics/1 ... /index.htm ) and is extremely applicable with GRE.
so, let's just write down first few terms of the series:
1 + 4/2 + 9/6 + 16/14 + 25/120 + 36/720 + ...
and try to estimate what's that:
~= 1 + 2 + 1.5 + 0.66 + 0.2 + 0.05 = 5.41.
stop right there and review your possible answers.
A: e~=2.7 < 5.41. out.
B: 2*e~=5.4. very close, let's check other options.
C: (e+1)(e-1)~=6.28 (probably the most time-consuming comp.) - too much. out.
D: e^2~=7.29. out.
E: out as well, we see that denominator increases way faster than numerator (not very rigorous, but works, right?)
so, the answer is B. I believe this might be not very profound solution, however it can save you a priceless minute or two on the real test.
opinions?