1/(1*3)+1/(3*5)+1/(5*7)+.+1/(2n-1)(2n+1)(n是正整数)
问题描述：
1/(1*3)+1/(3*5)+1/(5*7)+.+1/(2n-1)(2n+1)(n是正整数)
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答
1/(1×3)+1/(3×5)+1/(5×7)+……+1/(2n-1)(2n+1)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+……+[1/(2n-1)-1/(2n+1)]/2
=[1-1/3+1/3-1/5+1/5-1/7+……+1/(2n-1)-1/(2n+1)]/2
=[1-1/(2n+1)]/2
=[2n/(2n+1)]/2
=n/(2n+1)