bluechococake6595 bluechococake6595
  • 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 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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