### A Close Match

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

### Prime Counter

A short challenge concerning prime numbers.

### The Right Volume

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

# The Root of the Problem

##### Age 16 to 18 ShortChallenge 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.