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[tex] \frac{(n+2!)}{(n+1)!} =? [/tex]

Răspuns :

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[tex]\rm \frac{(n+2)!}{(n+1)!}=\frac{(n+1)!*(n+2)}{(n+1)!}=n+2[/tex]
[tex](n+2)!=1\cdot2\cdot3\cdot .... \cdot (n+2)\\
\\ (n+1)!=1\cdot2\cdot3\cdot .... \cdot (n+1)\\
\\ \\
\\ \frac{(n+2)!}{(n+1)!}=\frac{(n+1)!\cdot (n+2)}{(n+1)!}=\\
\\=\frac{n+2}{1}=n+2\\
\\ \\
\\ ( \frac{(n+2)!}{(n+1)!}=\frac{1\cdot2\cdot3\cdot .... \cdot (n+1)\cdot (n+2)}{1\cdot2\cdot3\cdot .... \cdot (n+1)}=n+2)[/tex]

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