Question

What is the maximum possible value of `k` for which 2013 can be written as a sum of `k` consecutive positive integers?

Answer 1

4025

Explanation:

Key points

Positive integer values.

`ul("Maximum")` count of `ul("consecutive")` values that are summed

To be a maximum count means that you have to start at the lowest positive value, which is 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mean value times the count of values = 2013

Starting at 1 means that the last value is the same as the count of values so we have:

`=> (1+k)/2=2013`

`=>1+k=4026`

`=>k=4025`