5 The function f is defined by
$$f ( r ) = 2 ^ { r } ( r - 2 ) \quad ( r \in \mathbb { Z } )$$
5
- Show that
$$\mathrm { f } ( r + 1 ) - \mathrm { f } ( r ) = r 2 ^ { r }$$
5
- Use the method of differences to show that
$$\sum _ { r = 1 } ^ { n } r 2 ^ { r } = 2 ^ { n + 1 } ( n - 1 ) + 2$$