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Question Number 182437 by akolade last updated on 09/Dec/22

Answered by qaz last updated on 09/Dec/22

$$\left(\begin{array}{c}n+2\\ r\end{array}\right)=\left[x^r\right]{(1+x)}^{n+2}=\left[x^r\right]({(1+x)}^n+2x{(1+x)}^n+x^2{(1+x)}^n)$$$$=\left[x^r\right]{(1+x)}^n+2\left[x^{r-1}\right]{(1+x)}^n+\left[x^{r-2}\right]{(1+x)}^n$$$$=\left(\begin{array}{c}n\\ r\end{array}\right)+2\left(\begin{array}{c}n\\ r-1\end{array}\right)+\left(\begin{array}{c}n\\ r-2\end{array}\right),by{egorychev}^{\prime }smethod$$

Commented by akolade last updated on 17/Dec/22

$$\mathrm{thank}\mathrm{you}\mathrm{so}\mathrm{much}$$

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