1/(2*7)+1/(7*12)+1/(12*17)+.1/(97*102)?
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![1/(2*7)+1/(7*12)+1/(12*17)+.1/(97*102)?](/uploads/image/z/389051-35-1.jpg?t=1%2F%282%2A7%29%2B1%2F%287%2A12%29%2B1%2F%2812%2A17%29%2B.1%2F%2897%2A102%29%3F)
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