It is given that $\mathrm{f}\left( r \right)=\left( 2r-1 \right){{3}^{r-1}}$. Show that

Question

It is given that $\mathrm{f}\left( r \right)=\left( 2r-1 \right){{3}^{r-1}}$. Show that $\mathrm{f}\left( r \right)-\mathrm{f}\left( r-1 \right)=\frac{4}{9}r{{3}^{r}}$.[2] Hence find an expression for $\sum\limits_{r=1}^{n}{\left( {{3}^{r}}+1 \right)r}$ in terms of $n$. You need not simplify your answer.[5]

Accepted Answer

$\frac{3}{4}[(2n-1)3^n + 1] + \frac{n}{2}(1+n)$

2023 VJC P2 Q1

2023 VJC P2 Q1

Video Solution:

Solution:

Solution locked