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Find a set on which the sequence $\sin\left(\left(1+\frac1{n}\right)^x\right)$ converge pointwise. Thanks for any help.

I think we are required to find for which values of $x$ does the sequence converge pointwise!

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    Try showing us where you got stuck, this way you learn way more then that we just give you the answer.2012-01-07
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    Notice that sin is continuous everywhere; so if $\left( 1 + \frac1n \right)^x$ converges, then the given sequence also would converge. Does this hint help?2012-01-07
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    yes it helps, thanks2012-01-07

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This is not as interesting as $\sin ((1+x)^n)$ would be...

Since $(1+1/n)\to 1$, we have $(1+1/n)^x\to 1^x=1$ regardless of the value of $x$. So the limit is $\sin 1 $ for all $x$.