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How do you prove that?

Here is hint or outline. You need to know that e is defined by taking the limit as n approaches infinity of terms (1 + 1/n)^n. Also, [limit of 1 + r/n)^n]= e^r. Notice that the only role of k is to use repeated multiplication. Compare given to the limit of P(n) = (1 + 10 ln(2)/n)^n as n grows. Notice the match to #1 above with understanding rate r = 10 ln(2) here. Recognize r = 10 ln(2) = ln(2^10) = ln(1024) so e^r = e^ln(1024) = 1024. So, original limit equals e^(10 ln(2)) = 1024. QED

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