Did you know that \(1225\) can be written as the sum of seven consecutive integers?
That is, \[1225=172+173+174+175+176+177+178\]
The notation below illustrates a mathematical short form used for writing the above sum. This notation is called Sigma Notation.
\[\sum_{i=172}^{178}i = 1225\]
How many ways can the number \(1225\) be expressed as the sum of an even number of consecutive positive integers?