In this question you must show detailed reasoning.
By using partial fractions show that \(\sum _ { r = 1 } ^ { n } \frac { 1 } { r ^ { 2 } + 3 r + 2 } = \frac { 1 } { 2 } - \frac { 1 } { n + 2 }\).
Hence determine the value of \(\sum _ { r = 1 } ^ { \infty } \frac { 1 } { r ^ { 2 } + 3 r + 2 }\). [0pt]
[BLANK PAGE]
A plane \(\Pi\) has the equation \(\mathbf { r } . \left( \begin{array} { r } 3 6 - 2 \end{array} \right) = 15 . C\) is the point \(( 4 , - 5,1 )\).
Find the shortest distance between \(\Pi\) and \(C\).
Lines \(l _ { 1 }\) and \(l _ { 2 }\) have the following equations.
\(l _ { 1 } : \mathbf { r } = \left( \begin{array} { l } 4 3 1 \end{array} \right) + \lambda \left( \begin{array} { r } - 2 4 - 2 \end{array} \right)\)
\(l _ { 2 } : \mathbf { r } = \left( \begin{array} { l } 5 2 4 \end{array} \right) + \mu \left( \begin{array} { r } 1 - 2 1 \end{array} \right)\)
Find, in exact form, the distance between \(l _ { 1 }\) and \(l _ { 2 }\). [0pt]
[BLANK PAGE]