2 (a) Use standard results from the List of Formulae (MF19) to show that

$$\sum _ { r = 1 } ^ { n } ( 7 r + 1 ) ( 7 r + 8 ) = a n ^ { 3 } + b n ^ { 2 } + c n$$

where $a , b$ and $c$ are constants to be determined.\\

(b) Use the method of differences to find $\sum _ { r = 1 } ^ { n } \frac { 1 } { ( 7 r + 1 ) ( 7 r + 8 ) }$ in terms of $n$.\\

(c) Deduce the value of $\sum _ { r = 1 } ^ { \infty } \frac { 1 } { ( 7 r + 1 ) ( 7 r + 8 ) }$.\\

\hfill \mbox{\textit{CAIE Further Paper 1 2020 Q2}}