For every positive integer n, the $n^{th}$ term of a sequence is given by $a_n = 1/n - 1/(n+1)$ . What is the sum of the first 100 terms of this sequence?

Correct answer marked below

1/101

99/100

100/101

Correct

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Explanation

Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.

Comments

VionaMay 7

Thanks, this one clicked once I wrote out a few terms.

SheetalMay 16

Same here. The pattern is actually pretty clean after the first three.

AnitaSep 19

Classic telescoping. I'd just be careful with the very last term — that's where I always slip.

HarshiSep 22

Yep, the last one doesn't cancel fully. Easy to miss under time pressure.

AadhithyaJun 16

I got this one but spent too long trying to compute terms directly. What's the quickest way to see the cancellation?

SanyamJun 17

Write the first three terms and look at what disappears. It's worth the 20 seconds.

NainaaJun 29

Don't compute decimals. Keep them as fractions and the pattern is obvious.

NaveenJun 12

Is this really a 505–555 level question? The algebra is simple, but the telescoping idea threw me at first.

What this question tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.

For every positive integer n, the nthn^{th}nth term of a sequence is given by an=1/n−1/(n+1)a_n = 1/n - 1/(n+1)an​=1/n−1/(n+1). What is the sum of the first 100 terms of this sequence?