1/(27)+1/(712)+1/(1217)+.1/(97102)?

来源：学生作业帮助网编辑：作业帮时间：2024/05/01 06:21:13

1/(2*7)+1/(7*12)+1/(12*17)+.1/(97*102)?
1/(2*7)+1/(7*12)+1/(12*17)+.1/(97*102)?

1/(2*7)+1/(7*12)+1/(12*17)+.1/(97*102)?
1/(2*7)+1/(7*12)+1/(12*17)+.1/(97*102)
=(1/5)*(1/2-1/7+1/7-1/12+1/12-1/17+.+1/97-1/102)
=(1/5)*(1/2-1/102)
=(1/5)*50/102
=10/102
=5/51

5/51 裂项相消