Sum (S) of first 100 terms of series 1, -1/2, 1/3, -1/4 and so on?

a) S<1
b) S>1
c) S=2
d) S=3
e) S>3

Pia -

The series 1 - 1/2 + 1/3 - 1/4... is the alternating harmonic series and converges to ln2 ~ .69. So the answer would be A. This question seems somewhat out of scope for the GMAT though I suppose you can see by inspection that the series has to converage somewhere between .5 and 1.

/Jeff

The easiest way to understand what Jeff has correctly explained is to use a number line. Plot the point 1, then subtract 1/2, which gives a point at 1/2. Then add 1/3, which results in a point between 1/2 and 1. Then subtract 1/4, which results in a point between the new point and 1/2. It will quickly become obvious that the final result has to be between 1/2 and 1.

Hope that helps!
-dan

It is very simple.

Your series can be rewritten as 1-(1/2-1/3) - (1/4-1/5) - so on
now see that each quantity within the bracket is positive so u r subtracting positive quantities from 1 so ans. is < 1.

Hope it helps