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For every positive integer n, the nth term of sequence is given by an= [#permalink]
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24 Apr 2016, 10:47
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inakihernandez wrote:
For every positive integer n, the nth term of sequence is given by an= 1/n - 1/n+1. What is the sum of the first 100 terms?
(a) 1 (b) 0 (c) 25 (d) 99/100 (e) 100/101
Hi, the moment you see the formula of nth number, it should tell you we are looking at a sequence .. \(a_1 = \frac{1}{1}-\frac{1}{2}\).. \(a_2= \frac{1}{2}-\frac{1}{3}\).. \(a_3 = \frac{1}{3}-\frac{1}{4}\).. ..... \(a_{99} = \frac{1}{99}-\frac{1}{100}\).. \(a_{100} = \frac{1}{100}- \frac{1}{101}\).. ADD all \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}..... \frac{1}{99}-\frac{1}{100}+\frac{1}{100}-\frac{1}{101} = 1-\frac{1}{101} = \frac{100}{101}\) so when you add all terms, what is left is \(1-\frac{1}{101} = \frac{100}{101}\).. E
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Re: For every positive integer n, the nth term of sequence is given by an= [#permalink]
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24 Apr 2016, 11:26
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inakihernandez wrote:
Hi chetan2u! thank you very much for your answer.
There is any way to calculate it using the formula (first term+last term)/2*number of terms?
because what I did as a first approach was a1= 1/2 ; a100= almost 0 => (1/2+0)/2*100= 25
No, don't use this formula here.. use it ONLY in an AP, where difference is common in consecutive numbers.. If you want to do approx, then too the terms should be atleast close to be called in AP
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Re: For every positive integer n, the nth term of sequence is given by an= [#permalink]
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14 May 2016, 14:43
Bunuel, chetan2u,
For me, the tricky part here is that the GMAT assumes that we know that (1- 1/2) + (1/2 - 1/4) + (1/4 - 1/8) ... (1/99-1/100)+(1/100-1/101) = 1 How can we know that? Is there any specific rule?
For every positive integer n, the nth term of sequence is given by an= [#permalink]
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14 May 2016, 20:09
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Jaikuz wrote:
Bunuel, chetan2u,
For me, the tricky part here is that the GMAT assumes that we know that (1- 1/2) + (1/2 - 1/4) + (1/4 - 1/8) ... (1/99-1/100)+(1/100-1/101) = 1 How can we know that? Is there any specific rule?
Many thanks in advance,
Jaime
Hi,
Except the first and the last term, all the other terms get cancelled out. So the only calculation required here is 1 - 1/101.
Re: For every positive integer n, the nth term of sequence is given by an= [#permalink]
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30 Oct 2016, 10:41
Vishvesh88 wrote:
Vyshakchetan2u : Why can't we use the Sum formula in this case? S100 = 100/2 * (2a + (100-1)d) ?
'Cuz if we do use, the answer comes to a value too far out from the answer choices, as per calculations.
Am i missing something?
The sum formula that you have mentioned can be applied only when the sequence is in arithmetic progression. The given sequence is not in AP and hence cannot be applied.
Re: For every positive integer n, the nth term of sequence is given by an= [#permalink]
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17 Dec 2017, 12:00
Hello,
Adding information regarding why this is not an AP (arithmetic progression) nor a GP (geometric progression). Do the math for: a1 = 1/2 a2 = 1/6 a3 = 1/12 a4 = 1/20 a5 = 1/30
If you try to put in any general term formula: a2 = a1 + r.1 => r = -1/3 Trying to apply for a3: a3 = 1/12 <> 1/2 + 2.(-1/3) The same goes with GP.
The largest is a(1) =1/2 and other terms become so small that they are not able to add together another 1/2 to overcome 1, but the sum is still +ve so crossout A,B,C.
Since we have to sum all this stuff and the last term a(100)=1/100*101 with prime number 101 in denominator, there is a huge chance that exactly 101 will stay in denominator. So the answer is (E).
p.s. This is not the best way to solve problems on GMAT, and you still have to learn the concept to be confident, but this is an example of how to make a smart guess and move on.
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For every positive integer n, the nth term of sequence is given by an=
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28 Apr 2018, 08:26
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63% (00:50) correct 
