15 (b) Use the method of differences to show that
$$\sum _ { r = 1 } ^ { n } \frac { 1 } { ( r + 2 ) ( r + 3 ) } = \frac { n } { 3 ( n + 3 ) }$$
| \multirow[t]{26}{*}{16} | Two matrices \(\mathbf { A }\) and \(\mathbf { B }\) satisfy the equation |
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Find the exact solution to the equation
$$\sinh \theta ( \sinh \theta + \cosh \theta ) = 1$$
| 18 | | \(\alpha , \beta\) and \(\gamma\) are the real roots of the cubic equation \(x ^ { 3 } + m x ^ { 2 } + n x + 2 = 0\) | | By considering \(( \alpha - \beta ) ^ { 2 } + ( \gamma - \alpha ) ^ { 2 } + ( \beta - \gamma ) ^ { 2 }\), prove that \(m ^ { 2 } \geq 3 n\) |
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