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December 1st, 2016, 01:49 PM   #1
ZMD
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Sequences

So the question was of two parts of which I proved the first one. The second part goes as follows:
ck= 2^k for k is even and ck= 1-1/k for which k is odd. I have to prove that lim ck=1.
I know that these two are subsequences and can prove for ck= 1-1/k approaches 1 but how to prove for ck=2^k? It would be of great help if someone could show this or overall how to solve this part.
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December 1st, 2016, 02:39 PM   #2
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$\displaystyle 2^k$ subsequence becomes infinite. There is something wrong with your statement of the problem.
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December 3rd, 2016, 11:38 AM   #3
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Quote:
Originally Posted by ZMD View Post
So the question was of two parts of which I proved the first one. The second part goes as follows:
ck= 2^k for k is even and ck= 1-1/k for which k is odd. I have to prove that lim ck=1.
I know that these two are subsequences and can prove for ck= 1-1/k approaches 1 but how to prove for ck=2^k? It would be of great help if someone could show this or overall how to solve this part.
You don't! The statement you are trying to prove not true. The sequence defined does not converge at all.
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