2019 Nov P1 Q3

Question 3

$3.1$	Without using a calculator, determine the value of: $\: \sum\limits_{y=3}^{10}\frac{\displaystyle 1}{\displaystyle y-2} - \sum\limits_{y=3}^{10}\frac{\displaystyle 1}{\displaystyle y-1}$	$(3)$
$3.2$	A steel pavilion at a sports ground comprises of a series of $12$ steps, of which the first $3$ are shown in the diagram below. Each step is $5\,m$ wide. Each step has a rise of $\frac{\displaystyle 1}{\displaystyle 3}\,m$ and has a tread of $\frac{\displaystyle 2}{\displaystyle 3}\,m$ , as shown in the diagram below.


	The open side (shaded on sketch) on each side of the pavilion must be covered with metal sheeting. Calculate the area (in $m^2$ ) of metal sheeting needed to cover both open sides.	$(6)$
		$\textbf{[9]}$