Did you know that \(1225\) can be written as the sum of ten consecutive integers?
That is, \[1225=118+119+120+121+122+123+124+125+126+127\]
The notation below illustrates a mathematical short form used for writing the above sum. This notation is called Sigma Notation.
\[\sum_{i=118}^{127}i = 1225\]
How many ways can the number \(1225\) be expressed as the sum of an odd number of consecutive positive integers?