Sequence SUM
This topic has expert replies
 Neilsheth2
 Senior  Next Rank: 100 Posts
 Posts: 65
 Joined: Sun Jun 03, 2012 8:58 am
 Thanked: 1 times
I guessed on this and moved on but need some help on how may I approach this question?
 Attachments

GMAT/MBA Expert
 [email protected]
 Elite Legendary Member
 Posts: 10392
 Joined: Sun Jun 23, 2013 6:38 pm
 Location: Palo Alto, CA
 Thanked: 2867 times
 Followed by:511 members
 GMAT Score:800
Hi Neilsheth2,
While this question looks complex, there's a great patternmatching 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
While this question looks complex, there's a great patternmatching 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
 Master  Next Rank: 500 Posts
 Posts: 410
 Joined: Fri Mar 13, 2015 3:36 am
 Location: Worldwide
 Thanked: 120 times
 Followed by:8 members
 GMAT Score:770
nth term = 1/n  1/(n + 1)Neilsheth2 wrote:I guessed on this and moved on but need some help on how may I approach this question?
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