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calculate-lim-n-k-1-n-1-n-k-0-lt-lt-1-




Question Number 166828 by qaz last updated on 28/Feb/22
calculate:   lim_(n→∞) Σ_(k=1) ^n (1/(n+k^α ))            .(0<α<1)
$$\mathrm{calculate}:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{n}+\mathrm{k}^{\alpha} }\:\:\:\:\:\:\:\:\:\:\:\:.\left(\mathrm{0}<\alpha<\mathrm{1}\right) \\ $$

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