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Sequence

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by greenwich » Tue Sep 28, 2010 3:32 pm
The sequence s1, s2, s3,.....sn,...is such that Sn= (1/n) - (1/(n+1)) for all integers n>=1. If k is a positive integer, is the sum of the first k terms of the sequence greater than 9/10?

1) k > 10
2) k < 19
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Source: — Data Sufficiency |
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by aimscore » Tue Sep 28, 2010 5:00 pm
greenwich,

u could check the following links.

https://www.beatthegmat.com/data-suffici ... 47978.html

https://gmatclub.com/forum/the-sequence- ... 99318.html.

It is always a good idea to google the question :) Most often than not, you are bound to find an explanation :)
Hope this helps.
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by shovan85 » Wed Sep 29, 2010 9:31 am
strongly agree with aimscore. however, still posting questions in the forum helps all a lot and the discussion makes the idea much clear. So keep posting and googling :)
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by gmatmachoman » Wed Sep 29, 2010 10:28 am
Sum = ( First term + last term /2) * n { formula to find sum when the enitities are in a sequence)

= {1 + 1/ n ( n+1)/ 2 } * n

= n ( n+1) +1 / 2 * ( n+1) --- eqn 1



St 1 : K > 10

So minimum K = 11

Put K = 11 in equation 1 :

(11 * 12 +1) /2 * ( 11+1)

133/24

133/24 is > 9/10

Sufficient

St 2:

K < 19

let K = 1 ; Sum = n ( n+1) +1 / 2 * ( n+1)
= 3/4 = 0.75

We have sum < 9/10

Let K = 18 ;Sum = 18 * 19 +1 / ( 2 * ( 18+1)
= 343 / 38
sum is > than 9/10
We have consistent values.
Insufficient

Pick A
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