Partial sums & series

Determine whether series converge or diverge based on their partial sums.


The n, t, h partial sum of the series S is given by
S, start subscript, n, end subscript, equals, space, start fraction, n, start superscript, 2, end superscript, plus, 1, divided by, n, plus, 1, end fraction.
Determine S.
Please choose from one of the following options.