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有2个数学题用简便做大哥大姐帮帮忙!

来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/05/25 09:51:39
有2个数学题用简便做大哥大姐帮帮忙!
⑴1/(1*)+1/(5*7)+······+1/(1995*1997)+1/(1997*1999)
⑵1/(2*7)+1/(7*12)+1/(12*17)·····+1/(92*97)+1/(97+102)
分数裂项
1/(1*5)+1/(3*5)+1/(5*7)+······+1/(1995*1997)+1/(1997*1999)
=(1/1-1/1999)*(1/2)
=999/1999
1/(2*7)+1/(7*12)+1/(12*17)·····+1/(92*97)+1/(97+102)
=(1/2-1/102)*(1/5)
=5/51