Thread: Problem 27
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Old June 24th, 2007, 12:37 AM
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Default Solution for 2)
2) If (s_n) is convergent then (s_n) is bounded and \lim_{n\to\infty}\frac{1}{n}=0, so \lim_{n\to\infty}\frac{s_n}{n}=0.
Then \displaystyle \lim_{n\to\infty}\left(1+\frac{s_n}{n}\right)^n=\lim_{n\to\infty}\left[\left(1+\frac{s_n}{n}\right)^{\frac{n}{s_n}}\right]^{\frac{s_n}{n}\cdot n}=e^{\lim_{n\to\infty}s_n}=e^s.