Summation of finite seriesEdexcel International A Level Further Maths: Mind map

Exam questions on Summation of finite series

1. A sequence has $r$th term $u_r=2r+3$, and $S_n$ is the sum of the first $n$ terms.
   Find the smallest value of $n$ for which $S_n>1000$.2 marks
2. Let $S_n=1\times3+2\times4+3\times5+\dots+n(n+2)$, the sum of the first $n$ terms of a series.
   Find the sum of the 6th to the 10th terms of the series, inclusive.2 marks
3. An orange display is built in layers. Layer $r$, counting from the top with $r=1,2,3,\dots$, is a square arrangement containing $r^2$ oranges.
   Find the number of oranges in layers $13$ to $20$ inclusive.3 marks