bài tập hoán vị

D

demon311

Ta có:

$(n+1)!=(n+1).n! = n.n!+n! \\
n!=(n-1+1).(n-1)!=(n-1).(n-1)!+(n-1)! \\
(n-1)!=(n-2).(n-2)!+(n-2)! \\
... \\
\Rightarrow (n+1)!=n.n!+(n-1).(n-1)!+...+1.1!+0!=\sum \limits^n_{k=1} k.k!+1 \\
\sum \limits^n_{k=1} k.k!=(n+1)!-1$
 
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