Method of differencesEdexcel A-Level Further Maths: Mind map

Exam questions on Method of differences

1. Let $u_r=\frac{1}{r(r+1)}$.
   Find the value of $\sum_{r=10}^{19}u_r$.2 marks
2. 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
3. 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