### 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?

# Seriesly

##### Age 16 to 18 ShortChallenge Level

Prove that
$$k \times k! = (k+1)! - k!$$ and sum the series
$$1 \times 1! + 2 \times 2! + 3 \times 3! +...+n \times n!$$

Did you know ... ?
A telecoping series is a series that can be written as the difference of two expressions in such a way that almost all the terms cancel with the following or preceding term leaving a few terms which can be combined to give the sum of the series. See the Wikipedia article Telescoping Series.