Determine whether each of the following sequences converge or not. In each case present a formal(adsbygoogle = window.adsbygoogle || []).push({});

explanation. If a sequence converges find the limit and if not determine whether there should be any

converging subsequences, and if so find more than one converging subsequences.

X_{k+1}= (k/k+2)X_{k}, where X_{1}= 1/2

Attempt: Now I was thinking of taking the (lim k-->∞ 1/(1+2/k) ) (lim k-->∞ X_{k}). In other words take the limits of the individual sequences and show that they converge, but I'm realizing I don't have an expression for X_{k}so I might not be able to do this. In the same breath if this sequence doesn't converge, would finding two subseqeunces through by fiddling with some numbers work?

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# Homework Help: Converging Sequnces

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