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Sequence S is the sequence of numbers a1, a2, a3, ... , an. [#permalink]
31 Jul 2020, 04:49
Question Stats:
55% (02:55) correct
44% (02:01) wrong based on 9 sessions
Sequence S is the sequence of numbers \(a_1, a_2, a_3,\) ... , \(a_n\). For each positive integer n, the \(n\)th number \(a_n\) is defined by \(a_n=\frac{n+1}{3n}\) . What is the product of the first 53 numbers in sequence S? A. \(\frac{2}{3^{53}}\) B. \(\frac{2}{3^{50}}\) C. \(\frac{2}{3^{49}}\) D. \(\frac{3}{2^{50}}\) E. \(\frac{2}{3^{25}}\)
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Founder
Joined: 18 Apr 2015
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Re: Sequence S is the sequence of numbers a1, a2, a3, ... , an. [#permalink]
31 Jul 2020, 04:54
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Re: Sequence S is the sequence of numbers a1, a2, a3, ... , an. [#permalink]
03 Aug 2020, 04:33
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an=(n+1)/3n
a1=2/3 a2=3/6 a3=4/9 a4=5/12 and so on
the product of all 53 terms will look like
=(2/3)*(3*6)*(4/9)*(5/12)*.... =(2/(3*1))*(3/(3*2))*(4/(3*3))*(5/(3*4))... Notice that each of the 53 terms in the denominator we have a 3 as a factor. So when all these 3's get multiplied together we get
(2*3*4*5*...53*54)/((3^53)*1*2*3*4...*53) The terms 2 to 53 get cancelled out with ones in the numerator leaving =54/(3^53) =(27*2)/(3^53) =((3^3)*2)/(3^53) =2/(3^50)
Final Answer: B




Re: Sequence S is the sequence of numbers a1, a2, a3, ... , an.
[#permalink]
03 Aug 2020, 04:33





