计算(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/99-1/100)等于多少

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计算(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/99-1/100)等于多少计算(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/99-1/100)等于

计算(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/99-1/100)等于多少
计算(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/99-1/100)等于多少

计算(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/99-1/100)等于多少
(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/99-1/100)
=1/2-1/3+1/3-1/4+...+1/99-1/100
=1/2-1/100
=49/100

(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/99-1/100)
=1/2-1/3+1/3-1/4+1/4-1/5+……+1/99-1/100
=1/2-1/100
=49/100

把括号去掉,中间的可以消掉,最后只剩下1/2-1/100=49/100

=1/2-1/100=49/100