2023 CJC Sigma Notation Tutorial Q7
Find the values of $A$, $B$ and $C$ such that for all values of $r$,
$1+{{r}^{2}}=A\left( r+2 \right)\left( r+1 \right)+B\left( r+1 \right)+C$.
Hence, prove by the method of differences that $\sum\limits_{r=1}^{n}{\left[ \left( 1+{{r}^{2}} \right)r! \right]}=n\left( n+1 \right)!$
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