Partial sums intro

The $n\text{th}$n, start text, t, h, end text partial sum of the series $\sum\limits_{n=1}^{\infty }{{{a}_{n}}}$sum, start subscript, n, equals, 1, end subscript, start superscript, infinity, end superscript, a, start subscript, n, end subscript is given by

$\displaystyle{{S}_{n}}=6-\frac{3}{{{n}^{2}}}$S, start subscript, n, end subscript, equals, 6, minus, start fraction, 3, divided by, n, squared, end fraction.

$\displaystyle\sum\limits_{n=1}^{9}{{{a}_{n}}}=$sum, start subscript, n, equals, 1, end subscript, start superscript, 9, end superscript, a, start subscript, n, end subscript, equals