Introdução a somas parciais

A $n\text{-ésima}$n, start text, negative, e, with, \', on top, s, i, m, a, end text soma parcial da série $\sum\limits_{n=1}^{\infty }{{{a}_{n}}}$sum, start subscript, n, equals, 1, end subscript, start superscript, infinity, end superscript, a, start subscript, n, end subscript é dada por

$\displaystyle{{S}_{n}}=6-\frac{3}{{{n}^{2}}}$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