3.1 Without using a calculator, determine the value of: $$\sum_{y=2}^{10} \frac{1}{y-1}$$ 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{1}{3} $ m and has a tread of $ \frac{2}{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 m²) of metal sheeting needed to cover both open sides.

NSC Mathematics Euclidean Geometry: 3.1 Without using a calculator,

3.1 Without using a calculator, determine the value of: $$\sum_{y=2}^{10} \frac{1}{y-1}$$ 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 - NSC Mathematics - Question 4 - 2019 - Paper 1

Question 4

$3.1-Without-using-a-calculator,-determine-the-value-of:---$$\sum_{y=2}^{10}-\frac{1}{y-1}$$--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-NSC Mathematics-Question 4-2019-Paper 1.png$

3.1 Without using a calculator, determine the value of: $$\sum_{y=2}^{10} \frac{1}{y-1}$$ 3.2 A steel pavilion at a sports ground comprises of a series of 12 step... show full transcript

Worked Solution & Example Answer:3.1 Without using a calculator, determine the value of: $$\sum_{y=2}^{10} \frac{1}{y-1}$$ 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 - NSC Mathematics - Question 4 - 2019 - Paper 1

Step 1

Without using a calculator, determine the value of: $$\sum_{y=2}^{10} \frac{1}{y-1}$$

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Answer

To solve this sum, we need to evaluate:

$\sum_{y=2}^{10} \frac{1}{y-1} = \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \frac{1}{9}$

Calculating each term:

$1 = 1$
$\frac{1}{2} = 0.5$
$\frac{1}{3} \approx 0.33$
$\frac{1}{4} = 0.25$
$\frac{1}{5} = 0.2$
$\frac{1}{6} \approx 0.167$
$\frac{1}{7} \approx 0.143$
$\frac{1}{8} = 0.125$
$\frac{1}{9} \approx 0.111$

Adding all these values:

$1 + 0.5 + 0.33 + 0.25 + 0.2 + 0.167 + 0.143 + 0.125 + 0.111 \approx 2.928$

Step 2

Calculate the area (in m²) of metal sheeting needed to cover both open sides.

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Answer

To calculate the area of metal sheeting required, we first need to find the total height and the overall width of the pavilion.

Step 1: Height of Pavilion

Each step has a rise of ( \frac{1}{3} ) m and there are 12 steps:

$\text{Total Height} = 12 \times \frac{1}{3} = 4 \, m$

Step 2: Width of Pavilion

Each step has a tread of ( \frac{2}{3} ) m and is 5 m wide. Thus, the width remains:

$\text{Total Width} = 5 \, m$

Step 3: Area Calculation

To cover both sides:

Area of one side = height x width = ( 4 , m \times 5 , m = 20 , m^2 )
For both sides = 2 x area of one side:

$\text{Total Area} = 2 \times 20 = 40 \, m^2$

Thus, the total area of metal sheeting needed is ( \text{40 m²} ).