Question

1乘3分之一加3乘5分之一加5乘7分之一一直加到二n加1，二n减1分之一等于多少

求结果

Answer 1

1/（1*3）+1/（3*5）+……+1/[(2n-1)(2n+1)]
=1/2*[(1-1/3)+(1/3-1/5)+...+1/(2n-1)-1/(2n+1)]
=1/2*(1-1/(2n+1)
=1/2*2n/(2n+1)
=n/2(n+1)

Answer 2

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