Which sequences converge to a limit as $n \rightarrow \infty$ ?
Choose all answers that apply:
A) $a_{n}=\frac{2^{n}}{n}$

B $b_{n}=\frac{3}{2^{n}}$
(c) $c_{n}=\frac{4^{n}}{n!}$

Question

Which sequences converge to a limit as $n \rightarrow \infty$ ?
Choose all answers that apply:
A) $a_{n}=\frac{2^{n}}{n}$

B $b_{n}=\frac{3}{2^{n}}$
(c) $c_{n}=\frac{4^{n}}{n!}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To determine if the sequence $a_n = \frac{2^n}{n}$ converges, we refer to the asksia-ll calculator result for the limit as $n ightarrow \infty$ of $\frac{2^n}{n}$... ‖ ‖ step 2 ⋮ The asksia-ll calculator indicates that $\lim_{n o \infty} \frac{2^n}{n} = \infty$, which means the sequence does not converge... ‖ ‖ step 3 ⋮ To determine if the sequence $b_n = \frac{3}{2^n}$ converges, we refer to the asksia-ll calculator result for the limit as $n ightarrow \infty$ of $\frac{3}{2^n}$... ‖ ‖ step 4 ⋮ The asksia-ll calculator indicates that $\lim_{n o \infty} \frac{3}{2^n} = 0$, which means the sequence converges to 0... ‖ ‖ step 5 ⋮ To determine if the sequence $c_n = \frac{4^n}{n!}$ converges, we refer to the asksia-ll calculator result for the limit as $n ightarrow \infty$ of $\frac{4^n}{n!}$... ‖ ‖ step 6 ⋮ The asksia-ll calculator indicates that $\lim_{n o \infty} \frac{4^n}{n!} = 0$, which means the sequence converges to 0... ‖ ***B*** and ***C*** ∻Key Concept∻ ⚹Convergence of a Sequence⚹ ∻Explanation∻ ⚹A sequence converges to a limit as $n ightarrow \infty$ if the terms of the sequence approach a specific value. The asksia-ll calculator results show that sequences $b_n$ and $c_n$ converge to 0, while sequence $a_n$ diverges to infinity.⚹◊What is the limit of the sequence $b_{n} = \frac{3}{2^{n}}$ as $n$ approaches infinity?⍭ Generate me a similar question◊

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