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let-S-n-k-0-n-1-3k-1-calculate-S-n-interms-of-H-n-with-H-n-k-1-n-1-k-




Question Number 35615 by abdo mathsup 649 cc last updated on 21/May/18
let  S_n  = Σ_(k=0) ^n   (1/(3k+1))  calculate S_n    interms of H_n    with H_n  =Σ_(k=1) ^n (1/k)
$${let}\:\:{S}_{{n}} \:=\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}} \\ $$$${calculate}\:{S}_{{n}} \:\:\:{interms}\:{of}\:{H}_{{n}} \:\:\:{with}\:{H}_{{n}} \:=\sum_{{k}=\mathrm{1}} ^{{n}} \frac{\mathrm{1}}{{k}} \\ $$

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