lim-n-n-n-1-sin-1-n-n-where-Q-is-equal-to-

Question Number 63921 by raj last updated on 11/Jul/19

\lim_{n \to \infty} {({(\frac{n}{n + 1})}^{α} + \sin \frac{1}{n})}^{n} where α \in Q

is equal to

Commented by kaivan.ahmadi last updated on 11/Jul/19

\sim {l i m}_{n \to \infty} ({(\frac{n}{n + 1})}^{α} - 1 + s i n \frac{1}{n}) (n) =

{l i m}_{n \to \infty} (\frac{n^{α + 1} - n {(n + 1)}^{α}}{{(n + 1)}^{α}} + n s i n \frac{1}{n}) =

\sim {l i m}_{n \to \infty} (\frac{- α n^{α}}{n^{α}} + n \times \frac{1}{n}) = - α + 1

Commented by raj last updated on 11/Jul/19

t h a n k y o u

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