query: Proving that $\left(1+\lambda/n\right)^n\to e^\lambda$
positive_passages.docid: 21380
positive_passages.text: Proof for $e^z = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{z}{x} \right)^x$
negative_passages.docid: 20467
negative_passages.text: Show that $(y_n)\in l^q$
negative_passages.docid: 18914
negative_passages.text: How prove this $A=\left(B-\frac{1}{110}I\right)^T\left(B+\frac{1}{110}I\right)$
negative_passages.docid: 100968
negative_passages.text: Why is $|e^{i \lambda z}| |e^{- \lambda y}|= |e^{- \lambda y}|$ here?
negative_passages.docid: 135694
negative_passages.text: Proving $\kappa^{\lambda} = |\{X: X \subseteq \kappa, |X|=\lambda\}|$
negative_passages.docid: 144819
negative_passages.text: Proving $P(n) =n^{\phi(n)} \prod\limits_{d \mid n} \left(\frac{d!}{d^d} \right)^{\mu(n/d)}$
negative_passages.docid: 136274
negative_passages.text: $n! \leq \left( \frac{n+1}{2} \right)^n$ via induction
negative_passages.docid: 32965
negative_passages.text: Proving that for infinite $\kappa$, $|[\kappa]^\lambda|=\kappa^\lambda$
negative_passages.docid: 48503
negative_passages.text: Proving : $ \bigl(1+\frac{1}{n+1}\bigr)^{n+1} \gt (1+\frac{1}{n})^{n} $
negative_passages.docid: 95450
negative_passages.text: Why does $\left(1+ 1/k\right)^k$ converge to $e$ as $k \to\infty$?
negative_passages.docid: 135731
negative_passages.text: Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
negative_passages.docid: 121548
negative_passages.text: proof of an inequality $ \left( 1+ \frac{x}{p} \right) ^{p}$
negative_passages.docid: 130765
negative_passages.text: Linear dependence of $\left\{x^{n}\,\colon\, n\in\mathbb{N}\right\}$
negative_passages.docid: 138107
negative_passages.text: Showing that $\left|\frac{z-a}{1-\bar{a}z}\right|=1$
negative_passages.docid: 154703
negative_passages.text: Use combinatorics to prove $L\left(n,k\right)=\sum_{j=0}^{n}{ n\brack j}{j\brace k}$
negative_passages.docid: 44940
negative_passages.text: Proving by induction that $1^3 + 2^3 + 3^3 + \ldots + n^3 = \left[\frac{n(n+1)}{2}\right]^2$
negative_passages.docid: 122481
negative_passages.text: proof of an identity for exponential function