### Series Sums

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

### Mystic Rose

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

### Slick Summing

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

# Natural Sum

##### Age 14 to 16 Challenge Level:

The picture illustrates the sum $1 + 2 + 3 + 4 = (4 \times5)/2$. 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. See the problem Picture Story .