Integration and differentiation of power series.

Problem

Let f, left parenthesis, x, right parenthesis, equals, start fraction, 1, divided by, 5, start superscript, 0, end superscript, end fraction, minus, start fraction, 2, divided by, 5, start superscript, 1, end superscript, end fraction, x, plus, start fraction, 3, divided by, 5, start superscript, 2, end superscript, end fraction, x, start superscript, 2, end superscript, plus, point, point, point, plus, left parenthesis, minus, 1, right parenthesis, start superscript, n, end superscript, start fraction, n, plus, 1, divided by, 5, start superscript, n, end superscript, end fraction, x, start superscript, n, end superscript, plus, point, point, point, equals, sum, start subscript, n, equals, 0, end subscript, start superscript, infinity, end superscript, left parenthesis, minus, 1, right parenthesis, start superscript, n, end superscript, start fraction, n, plus, 1, divided by, 5, start superscript, n, end superscript, end fraction, x, start superscript, n, end superscript.
Evaluate space, integral, start subscript, 0, end subscript, start superscript, 1, end superscript, f, left parenthesis, x, right parenthesis, space, d, x, space.
  • 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
Get 3 answers correct in a row