急呀,帮忙计算一下.要过程1/101*103+1/103*105+1/105*107+.1//199*201

1/101*103=(1/100-1/103)/2
1/103*105=(1/103-1/105)/2
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1/199*201=(1/199-1/201)/2
所以原式=(1/2)*(1/100-1/103+1/103-1/105+....+1/107-1/109+1/109- 1/201)
=(1/2)*(1/101-1/201)
=50/(101*201)

原式=1/2（1/101-1/103+1/103-1/105+1/105-1/107+.-1/109+1/109-1/201)=50/(201*101),每个1/n*(n+2)都可以分解为1/2[1/n-1/(n+2)]