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