Hi vipinsharma,

This question is either badly worded or incomplete...

We're asked for the sum of the first 40 terms...

I believe that the "intent" of this prompt is that the sequence (of 6 terms) is repeating....
1/2 + 1/3 -1/4
-1/2 -1/3 + 1/4
....
1/2 + 1/3 - 1/4
-1/2 - 1/3 + 1/4
etc.

If that IS the case, then every set of 6 terms "offsets" and sums to 0.

This means that we can ignore the first 36 terms (since that would be 6 full sets of 6 terms; that sum would be 0). We'll focus on the final 4 terms of the first 40 terms...

1/2 + 1/3 - 1/4 - 1/2....

The 1/2 and -1/2 offset, so we're left with...

1/3 - 1/4

For this we need a common denominator...

4/12 - 3/12 = 1/12

GMAT assassins aren't born, they're made,
Rich