Given that $\mathrm{f}\left( r \right)=\frac{r}{{{2}^{r}}}$. By considering $\mathrm{f}\left( r+1 \r

Question

Given that $\mathrm{f}\left( r \right)=\frac{r}{{{2}^{r}}}$. By considering $\mathrm{f}\left( r+1 \right)-\mathrm{f}\left( r \right)$, find $\sum\limits_{r=1}^{n}{\frac{1-r}{{{2}^{r+1}}}}$.[3] Find $\sum\limits_{r=3}^{n}{\frac{r}{{{2}^{r+2}}}}$.[3]

Accepted Answer

(i) $\frac{n+1}{{{2}^{n+1}}}-\frac{1}{2}$ (ii) $\frac{1}{4}-\frac{n+2}{{{2}^{n+2}}}$

2018 RVHS Promo Q4

2018 RVHS Promo Q4

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