1/(101*103)+1/(103*105)+1/(105*107)+.+1/(199*201)
问题描述：
1/(101*103)+1/(103*105)+1/(105*107)+.+1/(199*201)
答
原式=(1/2)*(1/103-1/105+1/105-1/107+1/107......+1/199-1/201)=1/2*(1/103-1/201)=49/(103*201)
答
1/(101*103)+1/(103*105)+1/(5*7)+1/(7*9)+……+1/(199*201)
裂项法
1/(101*103)=1/2*(1/101-1/103)
1/(103*105)=1/2*(1/103-1/105)
.
1/(199*201)=1/2(1/199-1/201)
原式
=1/2(1/101-1/103+1/103-1/105.+1/199-1/201)
=1/2(1/101-1/201)
=50/(101*201)
=50/20301