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### Number and algebra

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### Working mathematically

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### For younger learners

# Series Sums

Let

$S_1 = 1$

$S_2 = 2 + 3$

$S_3 = 4 + 5 + 6$, $\cdots$

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Age 14 to 16

Challenge Level

- Problem
- Student Solutions

Let

$S_1 = 1$

$S_2 = 2 + 3$

$S_3 = 4 + 5 + 6$, $\cdots$

Calculate $S_{17}$

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural numbers.

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.