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

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16-06-2017
Mathematics

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

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LammettHash LammettHash · Answer 1 · 2017-06-16T16:48:10+02:00

LammettHash LammettHash

16-06-2017

[tex]\displaystyle\sum_{n\ge0}\frac{(\ln3)^n}{n!}=e^{\ln3}=3[/tex]

which follows from the power series representation for [tex]e^x[/tex],

[tex]e^x=\displaystyle\sum_{n\ge0}\frac{x^n}{n!}[/tex]

and taking [tex]x=\ln3[/tex].

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