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Calculus, all content (2017 edition)

Course: Calculus, all content (2017 edition) > Unit 7

Lesson 16: Challenge series exercises
Math
Calculus, all content (2017 edition)
Series
Challenge series exercises
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Series estimation challenge

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Problem

The infinite series for space, e, start superscript, x, end superscript, space is given by
e, start superscript, x, end superscript, equals, 1, plus, x, plus, start fraction, x, squared, divided by, 2, !, end fraction, plus, start fraction, x, cubed, divided by, 3, !, end fraction, plus, point, point, point, plus, start fraction, x, start superscript, n, end superscript, divided by, n, !, end fraction, plus, point, point, point
On the interval space, minus, 1, is less than or equal to, x, is less than or equal to, 0, what is the minimum number of terms necessary to approximate the value of space, e, start superscript, x, end superscript, space accurate to the nearest space, 0, point, 01?
  • 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
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