Express $\frac{{{r}^{2}}+7r+11}{\left( r+4 \right)!}$ in the form \(\frac{A}{\left( r+2 \right)!}+

Question

Express $\frac{{{r}^{2}}+7r+11}{\left( r+4 \right)!}$ in the form $\frac{A}{\left( r+2 \right)!}+\frac{B}{\left( r+4 \right)!}$ where $A$ and $B$ are constants to be found. Hence show that $\sum\limits_{r=1}^{n}{\frac{{{r}^{2}}+7r+11}{\left( r+4 \right)!}}=\frac{5}{24}-\frac{n+5}{\left( n+4 \right)!}$.

Accepted Answer

$\frac{5}{24} - \frac{n+5}{(n+4)!}$

Method of Difference Q5

Method of Difference Q5

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