求证1/(2*3)+1/(3*5)+1/(4*7)+...+-查字典问答网

来自刘俊民的问题

　　求证1/(2*3)+1/(3*5)+1/(4*7)+...+1/((n+1)(2n+1))

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2020-08-04 08:20

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戴弋

　　1/(2*3)+1/(3*5)+1/(4*7)+...+1/[(n+1)(2n+1)]=1/6+1/(3*5)+1/(4*7)+...+1/[(n+1)(2n+1)]=1/6+1/2*{1/(3*2.5)++1/(4*3.5)+...+1/[(n+1)(n+0.5)]}

2020-08-04 08:25:49

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