Method of differencesEdexcel A-Level Further Maths: Flashcards

What these 12 flashcards ask

What does the method of differences rely on?
\sum{r=1}^{n}\left[f(r)-f(r+1)\right]?
Partial fractions of \frac1{r(r+1)}?
\sum{r=1}^{n}\frac1{r(r+1)}?
Partial fractions of \frac1{(r+1)(r+3)}?
How many terms survive when the fractions are two places apart?
\sum{r=1}^{n}\left[(r+1)^3-r^3\right]?
\sum{r=a}^{n}\left[f(r)-f(r+1)\right]?
\frac1{r^2}-\frac1{(r+1)^2} as a single fraction?
\sum{r=1}^{\infty}\frac1{r(r+1)}?
Partial fractions of \frac1{r(r+1)(r+2)}?
How do you find A and B in \frac1{(r+1)(r+3)}=\frac A{r+1}+\frac B{r+3}?

Exam questions on Method of differences

Let $u_r=\frac{1}{r(r+1)}$ .
Find the value of $\sum_{r=10}^{19}u_r$ .2 marks
For all values of $r$ , $(r+1)^3-r^3=3r^2+3r+1$ .
Hence find the value of $\sum_{r=11}^{20}\left(3r^2+3r+1\right)$ .2 marks
Let $u_r=\frac{1}{(r+1)(r+3)}$ .
Express $u_r$ in the form $\frac{A}{r+1}+\frac{B}{r+3}$ , where $A$ and $B$ are constants to be found.3 marks

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).