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What is the sum of the series 1 + ln3 + (ln3)^2/2!?

What is the sum of the series 1 + ln3 + (ln3)^2/2!?
asked 142k views
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What is the sum of the series 1 + ln3 + (ln3)^2/2!?

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User Woodham
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1 Answer

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\displaystyle\sum_(n\ge0)((\ln3)^n)/(n!)=e^(\ln3)=3

which follows from the power series representation for
e^x,


e^x=\displaystyle\sum_(n\ge0)(x^n)/(n!)

and taking
x=\ln3.
answered
User Svkvvenky
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