1/2+1/6+1/12+.1/9900

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1/2+1/6+1/12+.1/99001/2+1/6+1/12+.1/99001/2+1/6+1/12+.1/9900答：原式=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(99*1

1/2+1/6+1/12+.1/9900
1/2+1/6+1/12+.1/9900

1/2+1/6+1/12+.1/9900
答：原式
=1/(1*2)+1/(2*3)+1/(3*4)+...+1/(99*100)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+...+(1/99-1/100)
=1-1/100
=99/100

1/2+1/6+1/12+.......1/9900
=1/2+（1/2-1/3）+（1/3-1/4）+.......+（1/99-1/100）
=1/2+1/2-1/3+1/3-1/4+.......+1/99-1/100
=1/2-1/100
=49/100