[理工] 遞迴

[tiger1029 (日向)]

https://i.imgur.com/RxG38SD.jpg

問一下這題怎算

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推 bochengchen: 同時除掉n(n+1)
→ ken2812221: bn = an / (n+1)
→ ken2812221: bn - bn-1 = 1/n -1/(n+1)
→ ken2812221: bn = bn-1 + 1/n - 1/(n+1)
→ ken2812221: bn = bn-2 + 1/(n-1) - 1/(n+1)
→ ken2812221: bn = b0 + 1/1 - 1/(n+1)
→ ken2812221: bn = 2 - 1/(n+1)
→ ken2812221: an = 2n + 1