delfoster03 delfoster03
  • 03-05-2022
  • Mathematics
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find maclaurin series

find maclaurin series class=

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LammettHash
LammettHash LammettHash
  • 03-05-2022

Recall the series expansion of the exponential function,

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{x^n}{n!}[/tex]

By comparison, the given sum is [tex]e^x[/tex] evaluated at x = ln(2), so

[tex]\displaystyle 1 + \ln(2) + \frac{\ln^2(2)}{2!} + \cdots = \sum_{n=0}^\infty \frac{\ln^n(2)}{n!} = e^{\ln(2)} = \boxed{2}[/tex]

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