### Weekly Challenge 43: A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

### Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

### Weekly Challenge 28: the Right Volume

Can you rotate a curve to make a volume of 1?

# Weekly Challenge 18: the Root of the Problem

##### Stage: 5 Short Challenge Level:

Find the sum of $$\frac{1}{\sqrt{1}+ \sqrt{2}}+ \frac{1}{\sqrt{2}+ \sqrt{3}} + \text{and so on up to}+\frac{1}{ \sqrt {99}+ \sqrt{100}}.$$

Can you invent any similar sums which have integer answers?
Did you know ... ?

Whilst this series can be summed using elementary methods mathematicians devise various ways in which the sums of series can be analysed. These are explored in greater detail in university analysis courses.