Упрости каждое выражение: \dfrac{1}{(n+2)!}-\dfrac{1}{n+1}!+\dfrac{1}{n}!= \dfrac{1-n(n+2)+(n+1)(n+2)}{(n+2)!}= \dfrac{1-n-2+n^2+n+2n+2}{(n+2)!}=\dfrac{n^2+2n+1}{(n+2)!}=\dfrac{(n+1)^2}{(n+2)!}. а) \dfrac{1}{n!}-\dfrac{1}{n+1}= ; б) \dfrac{1}{(n+2)!}-\dfrac{1}{(n+1)!}= ; в) \dfrac{1}{(n+1)!}+\dfrac{1}{(n-1)!}-\dfrac{1}{n!}= .

Задание

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Упрости каждое выражение:

\(\dfrac{1}{(n+2)!}-\dfrac{1}{n+1}!+\dfrac{1}{n}!=\)

\(\dfrac{1-n(n+2)+(n+1)(n+2)}{(n+2)!}=\)

\(\dfrac{1-n-2+n^2+n+2n+2}{(n+2)!}=\dfrac{n^2+2n+1}{(n+2)!}=\dfrac{(n+1)^2}{(n+2)!}.\)

а) \(\dfrac{1}{n!}-\dfrac{1}{n+1}=\) [ ];

б) \(\dfrac{1}{(n+2)!}-\dfrac{1}{(n+1)!}=\) [ ];

в) \(\dfrac{1}{(n+1)!}+\dfrac{1}{(n-1)!}-\dfrac{1}{n!}=\) [ ].