1/12+1/23+1/34+1/45+1/56+.+1/9899+1/99100

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1/12+1/23+1/34+1/45+1/56+.+1/9899+1/991001/12+1/23+1/34+1/45+1/56+.+1/9899+1/991001/12+1/23+1/34+1/4

1/12+1/23+1/34+1/45+1/56+.+1/9899+1/99100
1/12+1/23+1/34+1/45+1/56+.+1/9899+1/99100

1/12+1/23+1/34+1/45+1/56+.+1/9899+1/99100
LZ漏了个乘号吧.
对于通项1/n*(n+1)=1/n-1/(n+1).然后把1,2,3,.99代替n,所得的式子全加起来,就得到原式=99/100