edited by
312 views
1 votes
1 votes

Let $f(x)=1-\sin x$ for $x \in \mathbb{R}$. Define
\[ a_{n}=\sqrt[n]{f\left(\frac{1}{n}\right) f\left(\frac{2}{n}\right) \ldots f\left(\frac{n}{n}\right)}. \]
Then

  1. $\left\{a_{n}\right\}_{n}$ converges to $0$
  2. $\left\{a_{n}\right\}_{n}$ diverges to $\infty$
  3. $\left\{a_{n}\right\}_{n}$ converges and $\displaystyle{}\lim _{n \rightarrow \infty} a_{n}>0$
  4. none of the other three options is correct
edited by

Please log in or register to answer this question.

Answer:

Related questions

1 votes
1 votes
0 answers
1
admin asked Sep 9, 2022
262 views
Answer whether the following statements are True or False.Let $a_{n} \geq 0$ for each positive integer $n$. If the series $\sum_{n=1}^{\infty} \sqrt{a_{n}}$ converges, th...
1 votes
1 votes
0 answers
4
admin asked Sep 9, 2022
185 views
What is the number of solutions of: \[ x=\frac{x^{2}}{50}-\cos \frac{x}{2}+2 \] in $[0,10]?$ $0$$1$$2$$\infty$