若(1/1x3)+(1/3x5)+(1/5x7)+ - 知识问答

若(1/1x3)+(1/3x5)+(1/5x7)+……+[1/(2n-1)(2n+1]=?用含有n的式子表示

2个回答

1/(2n-1)(2n+1)
=1/2*2/(2n-1)(2n+1)
=1/2*[(2n+1)-(2n-1)]/(2n-1)(2n+1)
=1/2*[(2n+1)/(2n-1)(2n+1)-(2n-1)/(2n-1)(2n+1)]
=1/2*[1/(2n-1)-1/(2n+1)]
所以原式=1/2*[1-1/3+1/3-1/5+……+1/(2n-1)-1/(2n+1)]
=1/2*[1-1/(2n+1)]
=n/(2n+1)

相关问题