发现神数9801

1/9801 = 0.00(010203040506070809101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979900)(repeat)

这是为什么呢?

原来,1/99 = sum_{n=1}^{n=inf} (1/100)^n,
而 1/9801 = (1/99)^2 = (1/100) sum_{n=1}^{n=inf} n (1/100)^n

ps1,其实我是看到有人提到1/998001想到的。

ps2,wolframalpha.com 还算错了,漏掉了98。

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