The sum of the series 2+3+4+5+....+n can be calculated using the formula for the sum of an arithmetic series:

S = n/2 * (first term + last term)

In this case, the first term is 2 and the last term is n. Therefore, the sum of the series is:

S = n/2 * (2 + n)

Simplifying further:

S = n/2 * (n + 2)

S = n^2/2 + n

Therefore, the sum of the series 2+3+4+5+....+n is n^2/2 + n.