2021 TJC P2 Q2
It is given that $\text{f}\left( r \right)=\frac{1}{r!}$ where $r$ is a positive integer.
(i)
Show that $\text{f}\left( r \right)-\text{f}\left( r+1 \right)=\frac{r}{\left( r+1 \right)!}$.
[1]
(ii)
The sum of the first $n$ terms of the series $\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+…$ is given by ${{S}_{n}}$. Find ${{S}_{n}}$ and explain why the series converges.
[4]
(iii)
By considering (ii) and using the standard series from the List of Formulae (MF26), find the exact value of $\sum\limits_{r=2}^{\infty }{\frac{r+2}{r!}}$.
[4]
Suggested Handwritten and Video Solutions
Share with your friends!
WhatsApp
Telegram
Facebook