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16) Find X

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Source: — Problem Solving |
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by beat_gmat_09 » Sat May 01, 2010 6:58 am
varunkh70 wrote:X=1/11+1/12+1/13+......+1/20 , what's the value of X ?

I don't have the answers to this but how would you approach this type of problem?
Source ?
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by varunkh70 » Tue May 11, 2010 5:03 pm
The source is Higher Secondary Mathematics by RS Agarwal. Any views?
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by this_time_i_will » Tue May 11, 2010 5:17 pm
One of the observation here is that with increasing denominator value, the contribution of terms towards sum decreases.
So a simple addition of first 1 or 2 or at the max 3 terms together with elimination of answer choices based on this simple addition should do the job.
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by rajeshsources » Tue May 11, 2010 11:17 pm
varunkh70 & all ----

As we know already,
the sum of integers is equal to
(n(F+L))/2, where n=no.of terms
F= first term
L= last term

Here, n = no.of terms = 20 - 11 = 9 but inclusive of 20, then total terms= 9+1=10.
F= 1/11; L=1/20
Substitute the same in the above formula,
(10(1/11+1/20))/2
== (5*(11+20))/220
== 31/44

Ans : 31/44, in decimals = rounded to 0.7


HTH, GOOD LUCK,

Thanks,
Rajesh,
Loves GMAT......!!!!
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