3
0
2
\end{array} \right] \quad \left[ \begin{array} { c }
5
- 1
3
\end{array} \right] \quad \left[ \begin{array} { l }
2
1
1
\end{array} \right]$$
2 Use the definitions of \(\cosh x\) and \(\sinh x\) in terms of \(\mathrm { e } ^ { x }\) and \(\mathrm { e } ^ { - x }\) to show that \(\cosh ^ { 2 } x - \sinh ^ { 2 } x \equiv 1\)
[0pt]
[2 marks]
3
- Given that
$$\frac { 2 } { ( r + 1 ) ( r + 2 ) ( r + 3 ) } \equiv \frac { A } { ( r + 1 ) ( r + 2 ) } + \frac { B } { ( r + 2 ) ( r + 3 ) }$$
find the values of the integers \(A\) and \(B\)
3 - Use the method of differences to show clearly that
$$\sum _ { r = 9 } ^ { 97 } \frac { 1 } { ( r + 1 ) ( r + 2 ) ( r + 3 ) } = \frac { 89 } { 19800 }$$