1/9x11+1/11x13+1/13x15+……+1/43x45=

题目

1/9x11+1/11x13+1/13x15+……+1/43x45=

答案

1/(9×11)+1/(11×13)+1/(13×15)+...+1/(43×45)
=(1/2)(1/9-1/11+1/11-1/13+1/13-1/15+...+1/43-1/45)
=(1/2)(1/9-1/45)
=2/45
一般的：1/[n(n+2)]=(1/2)[1/n -1/(n+1)]
1/[n(n+k)]=(1/k)[1/n -1/(n+k)]