Solve some problems related to sequence, series, and their partial sums.

Problem

The n, t, h partial sum of the series sum, start subscript, n, equals, 1, end subscript, start superscript, infinity, end superscript, a, start subscript, n, end subscript is given by
S, start subscript, n, end subscript, equals, 6, minus, start fraction, 3, divided by, n, start superscript, 2, end superscript, end fraction.
sum, start subscript, n, equals, 1, end subscript, start superscript, 9, end superscript, a, start subscript, n, end subscript, equals
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4