Determine or find out if the subsequent series is convergent or divergent.  If it converges find out its value.

Solution

To find out if the series is convergent we first requirement is to get our hands on a formula for the common term in the sequence of partial sums.

This is a well known series and its value can be displayed to be,

Thus, to find out if the series is convergent we will first require to see if the sequence of partial sums,

{n (n+1) / 2}^∞_n=1

is convergent/divergent.  That's not so much hard in this case.  The limit of the sequence terms is,

Hence, the sequence of partial sums diverges to ∞ and thus the series as well diverges.