Consider the sequence {an}1 where 1 1 an = 1++ The goal of this problem is to prove this sequence diverges to o. (a) Prove that for all k E Z with k > o 1 1 1 + + 2k + 2 1 + 2k 2k +1 2k+1 2 (b) Use (a) to prove that for all m E N a2m–1 >. (c) Deduce that {an}1 diverges to o.

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A: See the handwritten solution

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A: Topic = Limits

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A: The given figure is -  We have to find the value of 'x'.

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A:

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Q: (6) Let f(n) = n +ak-ın k−1 + ... + a1n+ao and g(n) + ··· +a1n+ao and g(n) = n™ +bm−1nm−1 ++b1n+bo…

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Q: 42. A sequence is recursively defined by T(0) = 1 T(1) = 2 T(n) = 2T(n – 1) + T(n – 2) for n > 2 %3D

A: Basis: Note that T(0)=1, T(1)=2 ,T(2) =2·2 + 1 = 5, T(3) = 2·5 + 2= 12, statement is truefor n…

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Q: 3. We found in class that if Cn counts the number of ways to make change (in standard coins) for n…

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.