(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+ ……+(1/19-1/20)的答案
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![(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+ ……+(1/19-1/20)的答案](/uploads/image/z/14292831-39-1.jpg?t=%281%2F2-1%2F3%29%2B%281%2F3-1%2F4%29%2B%281%2F4-1%2F5%29%2B+%E2%80%A6%E2%80%A6%2B%EF%BC%881%2F19-1%2F20%EF%BC%89%E7%9A%84%E7%AD%94%E6%A1%88)
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(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+ ……+(1/19-1/20)的答案
(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+ ……+(1/19-1/20)的答案
(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+ ……+(1/19-1/20)的答案
1/2-1/3)+(1/3-1/4)+(1/4-1/5)+ ……+(1/19-1/20)的第二项-1/3与第三项+1/3抵消为0,依此类推,只剩下头尾1/2和-1/20,所以(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+ ……+(1/19-1/20=1/2-1/20=9/20