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Non-Numerical proof of $e<\pi$

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#calculus #geometry #inequality #pi #eulers-number-e
407
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Finding limit from Squeeze theorem: $\lim\limits_{n\to\infty} \left(\frac{2n-5}{3n+1}\right)^n$

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#real-analysis #sequences-and-series #limits #exponential-function #eulers-number-e
151
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Limit of $a_n=(1- \frac{1}{n})^n$ as $n\rightarrow \infty$

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#calculus #sequences-and-series #limits #eulers-number-e
11.1k
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Why is Euler's number $2.71828$ and not anything else?

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#calculus #logarithms #irrational-numbers #eulers-number-e
1.3k
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What is the nature of $e^{ix}$, real or complex?

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#complex-numbers #exponential-function #real-numbers #eulers-number-e
115
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Meaning of Maclaurin expansion of $e$

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#sequences-and-series #taylor-expansion #recreational-mathematics #eulers-number-e
185
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Inequality involving $e$: $\binom{n}{k} < \frac{1}{e}\big(\frac{en}{k}\big)^k$

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#inequality #exponential-function #binomial-coefficients #eulers-number-e
431
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weird properties of complex exponentials: $e^{i 2 \pi f(x)} = 1$

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#complex-analysis #complex-numbers #eulers-number-e
592
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Is $\left(1+\frac1n\right)^{n+1/2}$ decreasing?

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#inequality #exponential-function #cauchy-schwarz-inequality #eulers-number-e
287
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Intuitively, why are the two limit definitions of $e^x$ equivalent?

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#continuity #exponential-function #exponentiation #intuition #eulers-number-e
159
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Intuitive understanding of Euler's Formula

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#complex-numbers #exponential-function #exponentiation #intuition #eulers-number-e
605
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$\sum_{n=0}^{\infty} \frac{\sin(nx)}{3^n}$

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#sequences-and-series #trigonometry #eulers-number-e
428
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Is there any online source for proofs than $(1+\frac{1}{n})^n$ and $(1+\frac{1}{x})^x$ is $e$?

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#limits #reference-request #eulers-number-e
784
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What is the derivative of $e^{i\pi}$?

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#derivatives #complex-numbers #pi #eulers-number-e
379
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Showing $\lim_{n\to \infty} \left( 1+\frac{1}{2n} \right)^n = \sqrt{e}$, intro to analysis

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#real-analysis #limits #eulers-number-e

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