The First Mathematics Scouts Problem of the week

So here goes the first Mathematics Scouts Problem of the week question :

A huge thank you to every problem proposer.


  • For all positive integers k show that the sum \sum_{n=1}^{\infty} \left ( \left ( \frac{1}{n!} \right )^k \right ) converges to an irrational number. (Proposed by the Mathematics Scouts team).


For more discussion about the mathematics scouts problem of the week visit the problem of the week discussion forum and archive page of the website.