1/2,1/6,1/12,1/20,......前100数的和怎么算
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![1/2,1/6,1/12,1/20,......前100数的和怎么算](/uploads/image/z/4086567-63-7.jpg?t=1%2F2%2C1%2F6%2C1%2F12%2C1%2F20%2C......%E5%89%8D100%E6%95%B0%E7%9A%84%E5%92%8C%E6%80%8E%E4%B9%88%E7%AE%97)
1/2,1/6,1/12,1/20,......前100数的和怎么算
1/2,1/6,1/12,1/20,......前100数的和怎么算
1/2,1/6,1/12,1/20,......前100数的和怎么算
1/2+1/6+1/12+1/20
=1*1/2+1/2*1/3+1/3*1/4+.
=1/2+1/2-1/3+1/3-1/4+.
=1-1/101
=100/101
原式=1/2+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+......(1/100-1/100)=100/101