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Prove-lim-n-n-k-n-1-n-1-k-1-k-1-2-




Question Number 159936 by qaz last updated on 22/Nov/21
Prove::   lim_(n→+∞) ^(−) nΣ_(k=n+1) ^n (((−1)^(k−1) )/k)=(1/2)
$$\mathrm{Prove}::\:\:\:\underset{\mathrm{n}\rightarrow+\infty} {\overline {\mathrm{lim}}n}\underset{\mathrm{k}=\mathrm{n}+\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{\mathrm{k}−\mathrm{1}} }{\mathrm{k}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$

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