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# If T= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + .........

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Intern
Joined: 23 Sep 2011
Posts: 12
If T= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + .........  [#permalink]

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02 Nov 2016, 10:30
2
6
00:00

Difficulty:

75% (hard)

Question Stats:

52% (02:16) correct 48% (02:34) wrong based on 110 sessions

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If T= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + ......... 1/[n(n+1)], for some positive integer n, what is the smallest value of n such that T>0,97?

(A) 29
(B) 30
(C) 31
(D) 32
(E) 33
Manager
Joined: 29 Aug 2008
Posts: 106
Re: If T= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + .........  [#permalink]

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02 Nov 2016, 11:26
4
1
T= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + ......... 1/[n(n+1)]

If we solve for n =1 , n =2 and n =3 we notice a trend

T(1) = 1/2

T(2) = 1/2 + 1/6 = 2/3

T(3) = 1/2 + 1/6 + 1/12 = 3/4

So T(n) = n/(n+1)

So we need the value of T(n) > 0.97

n/(n+1) > 0.97

Solving this we get n > 32.33

Option E
##### General Discussion
Director
Joined: 14 Nov 2014
Posts: 599
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: If T= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + .........  [#permalink]

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03 Nov 2016, 01:22
we can break the T as : (n + 1 -n)/n(n+1)----for n=1 to n
1/n - 1/ n + 1
plug value ,1,2..n we will get a pattern
1-1/2---for 1
1/2-1/3--for 2
1/3-1/4--for 4
now work with options..
for 31,T =1- 1/32=30/31=0.968
for 32,T=1-1/33=0,9696
for 33,T=1-1/34=33/34-0.97
Manager
Joined: 17 Aug 2012
Posts: 122
Location: India
Concentration: General Management, Strategy
Schools: Copenhagen, ESMT"19
GPA: 3.75
WE: Consulting (Energy and Utilities)
Re: If T= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + .........  [#permalink]

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26 Feb 2017, 21:53
T(N)= ( 1 -1/2 ) + (1/2 -1/3 ) + (1/3 -1/4 )..........((1/N )-1/(N+1))

T(N) =(1- 1/(N+1))

T(N) > 0.97

1 - 1/(N+1) > 097

1/(N+1) > .03

N+1 > 33.33

N > 32.33
Re: If T= 1/(1*2) + 1/(2*3) + 1/(3*4) + 1/(4*5) + .........   [#permalink] 26 Feb 2017, 21:53
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