Sequence SUM

[Neilsheth2]

I guessed on this and moved on but need some help on how may I approach this question?

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Hi Neilsheth2,

While this question looks complex, there's a great pattern-matching shortcut built into it - to recognize the pattern, you'll likely have to do a bit of work on the pad though.

We're asked for the sum of the first 100 terms in the given sequence, but the GMAT doesn't really expect you to add up all of that work by hand. I'm going to write down the first few terms as a reference, but I'm NOT going to do any of the math yet....

N=1 --> 1/1 - 1/2
N=2 --> 1/2 - 1/3
N=3 --> 1/3 - 1/4
N=4 --> 1/4 - 1/5
Etc.

Notice that when we subtract a fraction, we end up adding it right back in the next calculation (re: -1/2....+1/2....-1/3....+1/3), so a lot of that math 'cancels out.' The only terms that WON'T cancel out are 1/1 and the very last term.... -1/101

Thus, the sum of those first 100 terms ends up totaling 1/1 - 1/101 = 100/101

Final Answer: D

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

[OptimusPrep]

I guessed on this and moved on but need some help on how may I approach this question?

nth term = 1/n - 1/(n + 1)
Sum of first 100 terms = ?

Always remember whenever you are required to find a sum of a large number of terms, either there will be a repetition, a series or the terms will cancel out each other.

1st term = 1 - 1/2
2nd term = 1/2 - 1/3
3rd term = 1/3 - 1/4
.
.
.
.
99th term = 1/99 - 1/100
100th term = 1/100 - 1/101

On addition, observe that the terms are cancelled out.
Sum = 1 - 1/101 = 100/101

Correct Option: D