Question

计算：1/1x3+1/3x5+1/5x7+.+1/31x33+1/33x35,

Answer 1

因为 an=1/[(2n-1)*(2n+1)] = 1/2 [1/(2n-1) - 1/(2n+1)]

所以,

1/1x3+1/3x5+1/5x7+.+1/31x33+1/33x35

= 1/2*[(1/1 - 1/3) + (1/3 - 1/5) + (1/5 - 1/7) + …… + (1/33 - 1/35)]

= 1/2*(1/1 - 1/35)

=1/2* 34/35

=17/35