1/2+1/6+1/12+1/20+1/30+.+1/9900=?

1/2+1/6+1/12+1/20+1/30+.+1/9900=?
1/2+1/6+1/12+1/20+1/30+.+1/9900=?

1/2+1/6+1/12+1/20+1/30+.+1/9900=?
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)+……+(1/99-1/100)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/99-1/100
中间抵消
=1-1/100
=99/100

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)+……+(1/99-1/100)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+……+1/99-1/100
中间抵消
=1-1/100
=99/100

1/2+1/6+1/12+1/20+1/30+......+1/9900
=1-1/2+1/3-1/3+1/4-1/4+1/5.....+1/99-1/100
=1-1/100
=99/100

=1/1*2+1/2*3+1/3*4+1/4*5+…+1/99*100
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+…+1/99-1/100
=1-1/100
=99/100

1/2=1-1/2
1/6=1/2-1/3
1/12=1/3-1/4
1/20=1/4-1/5
1/9900=1/99-1/100
原式=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+。。。。。。+1/99-1/100
=1-1/100
=99/100