1/2,1/6,1/12,1/20,......前100个数的和怎么算

1/2,1/6,1/12,1/20,......前100个数的和怎么算
1/2,1/6,1/12,1/20,......前100个数的和怎么算

1/2,1/6,1/12,1/20,......前100个数的和怎么算
原式=1/2+1/6+1/12+1/20+1/1/30+1/42+……+1/(10100)
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+.+1/(100×101)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7+.+1/100-1/101
=1-1/101
=100/101

1/2+1/6+1/12+...+1/100*101
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/100-1/101)
=1-1/101
=100/101

1/2 +1/2-1/3 +1/3-1/4....+1/100-1/101
=1-1/101
=100/101

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