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The sequence s1, s2, s3,.....sn,...is such that Sn= [#permalink]
 26 Apr 2012, 07:14
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I don't know whether these problems have already been posted on the site, since I couldn't find the answers I will post them. 1) The sequence s_1, s_2, s_3, ..., s_n, ... is such that s_n=1/n - 1/n+1 for all integers n\geq 1. If k is a positive Integer, is the sum of the first k terms of the sequence greater than [fraction]{9}{10}[/fraction]? (1) k > 10 (2) k < 19 2) In the sequence x_0, x_1, x_2, ..., x_n, each term from x_1 to x_kis 3 greater than the previous term, and each term from x_k+1 to x_nis less than the previous term, where n and k are positive integers and k< n. If x_0 = x_n = 0 and if x_k = 15, what is the value of n? A) 5 B) 6 C) 9 D) 10 E) 15 Please elaborate these problems as simple as possible! Thank you! 
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Last edited by Bunuel on 26 Apr 2012, 07:54, edited 1 time in total.
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Re: Two sequence problems [#permalink]
26 Apr 2012, 07:54
Stiv wrote: I don't know whether these problems have already been posted on the site, since I couldn't find the answers I will post them. 1) The sequence s_1, s_2, s_3, ..., s_n, .., is such that [m]s_n=1/n - 1/n+1 for all integers n\geq 1. If k is a positive Integer, is the sum of the first k terms of the sequence greater than [fraction]{9}{10}[/fraction]? (1) k > 10 (2) k < 19 2) In the sequence x_0, x_1, x_2, ..., x_n, each term from x_1 to x_kis 3 greater than the previous term, and each term from x_k+1 to x_nis less than the previous term, where n and k are positive integers and k< n. If x_0 = x_n = 0 and if x_k = 15, what is the value of n? A) 5 B) 6 C) 9 D) 10 E) 15 Please elaborate these problems as simple as possible! Thank you! Two things: 1. Please post one question per topic; 2. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/
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Re: The sequence s1, s2, s3,.....sn,...is such that Sn= [#permalink]
26 Apr 2012, 07:56
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? Given: s_n=\frac{1}{n}-\frac{1}{n+1} for n\geq{1}. So: s_1=1-\frac{1}{2}; s_2=\frac{1}{2}-\frac{1}{3}; s_3=\frac{1}{3}-\frac{1}{4}; ... If you sum the above 3 terms you'll get: s_1+s_2+s_3=(1-\frac{1}{2})+(\frac{1}{2}-\frac{1}{3})+(\frac{1}{3}-\frac{1}{4})=1-\frac{1}{4} (everything but the first and the last numbers will cancel out). So the sum of first k terms is fgiven by the formula sum_k=1-\frac{1}{k+1}. Question: is sum_k=1-\frac{1}{k+1}>\frac{9}{10}? --> is \frac{k}{k+1}>\frac{9}{10}? --> is k>9? (1) k > 10. Sufficient. (2) k < 19. Not sufficient. Answer: A. In case of any question please post it here: the-sequence-s1-s2-s3-sn-is-such-that-sn-1-n-103947.html
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Re: The sequence s1, s2, s3,.....sn,...is such that Sn= [#permalink]
26 Apr 2012, 07:57
In the sequence x_0, \ x_1, \ x_2, \ ... \ x_n, each term from x_1 to x_k is 3 greater than the previous term, and each term from x_{k+1} to x_n is 3 less than the previous term, where n and k are positive integers and k<n. If x_0=x_n=0 and if x_k=15, what is the value of n?A.5 B. 6 C. 9 D. 10 E. 15 Probably the easiest way will be to write down all the terms in the sequence from x_0=0 to x_n=0. Note that each term from from x_0=0 to x_k=15 is 3 greater than the previous and each term from x_{k+1} to x_n is 3 less than the previous term: So we'll have: x_0=0, 3, 6, 9, 12, x_k=15, 12, 9, 6, 3, x_n=0. So we have 11 terms from x_0 to x_n thus n=10. Answer: D. In case of any question please post it here: in-the-sequence-x0-x1-x2-xn-each-term-from-x1-to-xk-126564.html
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Re: The sequence s1, s2, s3,.....sn,...is such that Sn=
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26 Apr 2012, 07:57
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