Somme partielle d'ordre n d'une série

Quel que soit $n$n, la somme partielle d'ordre $n$n de la série $\sum\limits_{n=1}^{+\infty }{{{a}_{n}}}$sum, start subscript, n, equals, 1, end subscript, start superscript, plus, infinity, end superscript, a, start subscript, n, end subscript est

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