1*2,2*3,3*4...99*100...你能算出前99项的倒数的和吗?
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1*2,2*3,3*4...99*100...你能算出前99项的倒数的和吗?
1*2,2*3,3*4...99*100...你能算出前99项的倒数的和吗?
1*2,2*3,3*4...99*100...你能算出前99项的倒数的和吗?
1/(1*2)+1/(2*3)+1/(3*4)+……+1/(98*99)+1/(99*100)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/98-1/99)+(1/99-1/100)
=1-1/2+1/2-1/3+1/3-1/4+……+1/98-1/99+1/99-1/100
=1-1/100=99/100