2023 DHS Promo Q7
2023 DHS Promo Q7 (a) It is given that $sumlimits_{r=1}^{n}{{{r}^{2}}=frac{1}{6}nleft( n+1 right)left( 2n+1 right)}$. (i) Find $sumlimits_{r=1}^{n}{left( {{2}^{r+1}}+3r-{{r}^{2}} right)}$ in the form $Aleft( {{2}^{n}}-1 right)+text{f}left( n right)$, where $A$ is