let-S-n-k-1-n-1-k-k-and-H-n-k-1-n-1-k-calculate-S-n-interms-of-H-n-2-find-lim-n-S-n-

Question Number 63164 by mathmax by abdo last updated on 29/Jun/19

$${let}\:{S}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\left(−\mathrm{1}\right)^{{k}} }{{k}}\:\:\:\:\:\:{and}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$$${calculate}\:{S}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left.\mathrm{2}\right){find}\:{lim}_{{n}\rightarrow+\infty} \:{S}_{{n}} \\ $$

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