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Natural Sum

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.

Slick Summing

Watch the video to see how Charlie works out the sum. Can you adapt his method?

A Little Light Thinking

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Series Sums

Age 14 to 16 Challenge Level:

Let
$S_1 = 1$
$S_2 = 2 + 3$
$S_3 = 4 + 5 + 6$, $\cdots$

Calculate $S_{17}$