2015 Sum Sequences

We can represent the number \(2014\) in various ways as the sum of positive consecutive integers:

\[97+98+99+100+...+115=2014\]

\[502+503+504+505=2014\]

The sum of consecutive integers with the highest number of terms that result in \(2014\) is:

\[12+13+14+15+16+17+...+61+62+63+64\]

We need to add up \(53\) consecutive numbers to get \(2014\).

What is the highest number of positive consecutive integers that we can add to get \(2015\).

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