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Limits of Sequences and Series

Convergence of Sequences


If sequence {an}\{a_n\} satisfies limn(2n1)an=17,\displaystyle \lim_{n \to \infty}(2n-1)a_n=17, what is the value of limnan\displaystyle \lim_{n \to \infty}a_n?

What value of NN satisfies

limn(1+52n)10n=eN? \lim_{n \rightarrow \infty} \left( 1 + \frac{5} { 2n} \right) ^ {10n} = e^{N} ?

What is the value of the limit limn1nsinn7π?\lim_{n \to \infty} \frac{1}{n} \sin \frac{n}{7}\pi?

What is limn2(n+6n+10n)\displaystyle \lim_{n \to \infty} 2(\sqrt{n+6}\sqrt{n+10}-n) ?

Evaluate limnsinnπ2.\lim_{n\to\infty}\sin\frac{n\pi}{2}.


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