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Find maclaurin series

Find maclaurin series-example-1
User Jessica
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Recall the series expansion of the exponential function,


\displaystyle e^x = \sum_(n=0)^\infty (x^n)/(n!)

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


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

User MattG
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