Calculus
Limits of Sequences and Series
If sequence \(\{a_n\}\) satisfies \[\displaystyle \lim_{n \to \infty}(2n-1)a_n=17,\] what is the value of \(\displaystyle \lim_{n \to \infty}a_n\)?
What value of \(N\) satisfies
\[ \lim_{n \rightarrow \infty} \left( 1 + \frac{5} { 2n} \right) ^ {10n} = e^{N} ? \]
What is the value of the limit \[\lim_{n \to \infty} \frac{1}{n} \sin \frac{n}{7}\pi?\]
What is \(\displaystyle \lim_{n \to \infty} 2(\sqrt{n+6}\sqrt{n+10}-n) \)?
Evaluate \[\lim_{n\to\infty}\sin\frac{n\pi}{2}.\]