find-the-value-of-n-1-n-1-n-2-n-1-we-give-n-1-n-1-n-2-pi-2-6-and-H-n-1-2-1-3-1-n-1-ln-n-s-1-n-s-is-the-constant-number-of-Euler-

Tinku Tara June 4, 2023 Limits 0 Comments

Question Number 25962 by abdo imad last updated on 16/Dec/17

find the value of Σ_(n=1) ^(n=∝) 1/_(n^2 (n+1)) we give Σ_(n=1) ^(n=∝) 1/_n 2= π^2 /6 and H_n =1+2^(−1) +3^(−1) +...+n^(−1) = ln(n) + s + θ(1/n) s is the constant number of Euler

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{{n}=\propto} \:\:\:\mathrm{1}/_{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)} \:\:{we}\:{give}\:\:\:\sum_{{n}=\mathrm{1}} ^{{n}=\propto} \mathrm{1}/_{{n}} \mathrm{2}=\:\pi^{\mathrm{2}} /\mathrm{6} \\ $$$${and}\:\:{H}_{{n}} =\mathrm{1}+\mathrm{2}^{−\mathrm{1}} +\mathrm{3}^{−\mathrm{1}} +…+{n}^{−\mathrm{1}} =\:{ln}\left({n}\right)\:+\:{s}\:+\:\theta\left(\mathrm{1}/{n}\right)\: \\ $$$${s}\:{is}\:{the}\:{constant}\:{number}\:{of}\:{Euler} \\ $$

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