Method of differences with partial fractionsAQA A-Level Further Maths: Mind map

Exam questions on Method of differences with partial fractions

1. Let $S_n=\sum_{r=1}^{n}\frac{1}{r(r+1)}$.
   Find the least value of $n$ for which $S_n>0.99$.2 marks
2. Let $u_r=r^3-(r-1)^3$ for positive integers $r$.
   Hence find $\sum_{r=11}^{20}\left(3r^2-3r+1\right)$.2 marks
3. Let $u_r=\frac{1}{(2r-1)(2r+1)}$ and $S_n=\sum_{r=1}^{n}u_r$.
   Express $u_r$ in partial fractions and hence show that $S_n=\frac{n}{2n+1}$.3 marks