- Problem
- Solution

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.

Let

$S_1 = 1$

$S_2 = 2 + 3$

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

Calculate $S_{17}$

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NRICH is part of the family of activities in the Millennium Mathematics Project.