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# Limits of Sequences and Series

Infinitely many mathematicians walk into a bar. The first says "I'll have a beer". The next ones say "I'll have half of the previous guy". The bartender pours out 2 beers and says "Know your limits".

# Convergence of Sequences

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 $\lim_{n\to\infty}\sin\frac{n\pi}{2}.$

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