Prove that the sequence $\left( 1+\frac{1}{n} \right)^n $ when $n$ $\to$ $\infty$ converges to a number between $2.7$ and $2.8$ using binomial theorem

score 98 · Answer 13 · 2026-04-16 17:00:39

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$\lim_{n \rightarrow \infty} (x_{n}^2 y_{n}) = (\lim_{n \rightarrow \infty } x_{n})^2 (\lim_{n \rightarrow \infty } y_{n})$

Published on 16 Apr 2026 - 17:00

score 84 · Answer 14 · 2026-04-15 12:48:38

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Question on convergence of $\sum_{n=0}^{\infty} \frac{(-1)^n2^{-n}}{n!}z^{2n+1}$

Published on 15 Apr 2026 - 12:48

score 84 · Answer 15 · 2026-04-16 02:19:56

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How to show $\lim_{x \rightarrow 0} ~\frac{\int_{0}^{x^2} e^{\sqrt{1+t}} dt}{x^2}=e?$

Published on 16 Apr 2026 - 2:19

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Prove that the sequence $\left( 1+\frac{1}{n} \right)^n $ when $n$ $\to$ $\infty$ converges to a number between $2.7$ and $2.8$ using binomial theorem

$\lim_{n \rightarrow \infty} (x_{n}^2 y_{n}) = (\lim_{n \rightarrow \infty } x_{n})^2 (\lim_{n \rightarrow \infty } y_{n})$

Question on convergence of $\sum_{n=0}^{\infty} \frac{(-1)^n2^{-n}}{n!}z^{2n+1}$

How to show $\lim_{x \rightarrow 0} ~\frac{\int_{0}^{x^2} e^{\sqrt{1+t}} dt}{x^2}=e?$

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