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.

Advertisements

Announcing the Mathematics Scouts Problem of the Week

Greetings to all,

We planned to start the Problem of the Week starting from Monday 14th May (and continues till … um… ad infinitum… what do you say ? ).

More details about it can be found at the problem of the week discussion and archive page of the website.