r_n - 1 <= n(r_{n-1} - 1) + 1, 令P_n = r_n - 1, P_2 = 5

P_n <= n((n-1)P{n-2}+1)+1 = n(n-1)P{n-2}+n+1 = ...... = n(n-1)...3P_2+n(n-1)...4+n(n-1)...5+......+1 = n!(1+1+1/2+1/(3!)+...+1/(n!))<=n!e

r_n<=n!e+1



【 在 hyk84 的大作中提到: 】
: 已知r_2=6, r_n≤n(r_{n-1}-1)+2, 求证 r_n≤n!e+1.
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