| Exam Board | Edexcel |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
|---|
| Topic | Proof by induction |
|---|
16. (a) Show that
$$\sum _ { r = 1 } ^ { n } ( r + 1 ) ( r + 5 ) = \frac { 1 } { 6 } n ( n + 7 ) ( 2 n + 7 ) .$$
(b) Hence calculate the value of \(\quad \sum _ { r = 10 } ^ { 40 } ( r + 1 ) ( r + 5 )\).
[0pt]
[P4 June 2004 Qn 1]