CalcS4

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Find the upper limit of the sequence \left\{x_{n}\right\}_{{n=1}}^{\infty },x_{n}=n\sin \left({\frac  {n\pi }{2}}\right)\,

The maximum of the sine function is 1 which occurs when n=4k+1,k=0,1,2,...\,. So

(4k+1)\to \infty \, as k\to \infty \, so the upper limit is \infty \,.



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