1/2+1/6+1/12+1/20+1/30+.+1/9900
＝(1-1/2) +(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6).+(1/98-1/99)+(1/99-1/100)
=1+(-1/2 +1/2)+(-1/3+1/3)+(-1/4+1/4)+(-1/5+1/5)+-1/6.+1/98+(-1/99+1/99)-1/100
=1-1/100
=99/100
数学题：1/2+1/6+1/12+.+1/9900=?
3个回答
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