Test convergence of $n^{1/2} sinleft(frac{1}{n^{1/2}}right)$ [closed]
Please help me show that
$$a_n = sqrt{n}sinleft(frac{1}{sqrt{n}}right)$$
converges to 1.
By my understanding, it should be drawn to either $infty$ or zero depending on which part "grows faster". I'm not sure how it can equal 1.
calculus sequences-and-series convergence infinity
edited Dec 2 '18 at 22:12
m0nhawk
1,48831228
asked Dec 2 '18 at 21:56
bowl
61
closed as off-topic by RRL, Saad, KReiser, Jyrki Lahtonen, Brahadeesh Dec 3 '18 at 4:26
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – RRL, Saad, KReiser, Jyrki Lahtonen, Brahadeesh
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
Please help me show that
$$a_n = sqrt{n}sinleft(frac{1}{sqrt{n}}right)$$
converges to 1.
By my understanding, it should be drawn to either $infty$ or zero depending on which part "grows faster". I'm not sure how it can equal 1.
calculus sequences-and-series convergence infinity
edited Dec 2 '18 at 22:12
m0nhawk
1,48831228
asked Dec 2 '18 at 21:56
bowl
61
closed as off-topic by RRL, Saad, KReiser, Jyrki Lahtonen, Brahadeesh Dec 3 '18 at 4:26
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – RRL, Saad, KReiser, Jyrki Lahtonen, Brahadeesh
If this question can be reworded to fit the rules in the help center, please edit the question.
2
Are you familiar with the (standard and fundamental) limit $lim_{t to 0} frac{sin t}{t} = 1$?
– T. Bongers
Dec 2 '18 at 21:56
add a comment |
Please help me show that
$$a_n = sqrt{n}sinleft(frac{1}{sqrt{n}}right)$$
converges to 1.
By my understanding, it should be drawn to either $infty$ or zero depending on which part "grows faster". I'm not sure how it can equal 1.
calculus sequences-and-series convergence infinity
edited Dec 2 '18 at 22:12
m0nhawk
1,48831228
asked Dec 2 '18 at 21:56
bowl
61
Please help me show that
$$a_n = sqrt{n}sinleft(frac{1}{sqrt{n}}right)$$
converges to 1.
By my understanding, it should be drawn to either $infty$ or zero depending on which part "grows faster". I'm not sure how it can equal 1.
calculus sequences-and-series convergence infinity
calculus sequences-and-series convergence infinity
edited Dec 2 '18 at 22:12
m0nhawk
1,48831228
asked Dec 2 '18 at 21:56
bowl
61
edited Dec 2 '18 at 22:12
m0nhawk
1,48831228
asked Dec 2 '18 at 21:56
bowl
61
edited Dec 2 '18 at 22:12
m0nhawk
1,48831228
edited Dec 2 '18 at 22:12
m0nhawk
1,48831228
edited Dec 2 '18 at 22:12
m0nhawk
1,48831228
1,48831228
asked Dec 2 '18 at 21:56
bowl
61
asked Dec 2 '18 at 21:56
bowl
61
asked Dec 2 '18 at 21:56
bowl
61
61
closed as off-topic by RRL, Saad, KReiser, Jyrki Lahtonen, Brahadeesh Dec 3 '18 at 4:26
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – RRL, Saad, KReiser, Jyrki Lahtonen, Brahadeesh
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by RRL, Saad, KReiser, Jyrki Lahtonen, Brahadeesh Dec 3 '18 at 4:26
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – RRL, Saad, KReiser, Jyrki Lahtonen, Brahadeesh
If this question can be reworded to fit the rules in the help center, please edit the question.
2
Are you familiar with the (standard and fundamental) limit $lim_{t to 0} frac{sin t}{t} = 1$?
– T. Bongers
Dec 2 '18 at 21:56
add a comment |
2
Are you familiar with the (standard and fundamental) limit $lim_{t to 0} frac{sin t}{t} = 1$?
– T. Bongers
Dec 2 '18 at 21:56
2
2
Are you familiar with the (standard and fundamental) limit $lim_{t to 0} frac{sin t}{t} = 1$?
– T. Bongers
Dec 2 '18 at 21:56
Are you familiar with the (standard and fundamental) limit $lim_{t to 0} frac{sin t}{t} = 1$?
– T. Bongers
Dec 2 '18 at 21:56
add a comment |
1 Answer
1
active
oldest
votes
HINT
Note that
$$a_n = sqrt{n}cdot sinfrac{1}{sqrt{n}}=frac{sinfrac{1}{sqrt{n}}}{frac{1}{sqrt{n}}}$$
with $frac{1}{sqrt{n}}to 0$ and then refer to the standard limit
- How to prove that $limlimits_{xto0}frac{sin x}x=1$?
answered Dec 2 '18 at 22:00
gimusi
1
Something wrong?
– gimusi
Dec 3 '18 at 7:44
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
HINT
Note that
$$a_n = sqrt{n}cdot sinfrac{1}{sqrt{n}}=frac{sinfrac{1}{sqrt{n}}}{frac{1}{sqrt{n}}}$$
with $frac{1}{sqrt{n}}to 0$ and then refer to the standard limit
- How to prove that $limlimits_{xto0}frac{sin x}x=1$?
answered Dec 2 '18 at 22:00
gimusi
1
Something wrong?
– gimusi
Dec 3 '18 at 7:44
add a comment |
HINT
Note that
$$a_n = sqrt{n}cdot sinfrac{1}{sqrt{n}}=frac{sinfrac{1}{sqrt{n}}}{frac{1}{sqrt{n}}}$$
with $frac{1}{sqrt{n}}to 0$ and then refer to the standard limit
- How to prove that $limlimits_{xto0}frac{sin x}x=1$?
answered Dec 2 '18 at 22:00
gimusi
1
Something wrong?
– gimusi
Dec 3 '18 at 7:44
add a comment |
HINT
Note that
$$a_n = sqrt{n}cdot sinfrac{1}{sqrt{n}}=frac{sinfrac{1}{sqrt{n}}}{frac{1}{sqrt{n}}}$$
with $frac{1}{sqrt{n}}to 0$ and then refer to the standard limit
- How to prove that $limlimits_{xto0}frac{sin x}x=1$?
answered Dec 2 '18 at 22:00
gimusi
1
HINT
Note that
$$a_n = sqrt{n}cdot sinfrac{1}{sqrt{n}}=frac{sinfrac{1}{sqrt{n}}}{frac{1}{sqrt{n}}}$$
with $frac{1}{sqrt{n}}to 0$ and then refer to the standard limit
- How to prove that $limlimits_{xto0}frac{sin x}x=1$?
answered Dec 2 '18 at 22:00
gimusi
1
edited Dec 3 '18 at 7:53
answered Dec 2 '18 at 22:00
gimusi
1
answered Dec 2 '18 at 22:00
gimusi
1
answered Dec 2 '18 at 22:00
gimusi
1
1
Something wrong?
– gimusi
Dec 3 '18 at 7:44
add a comment |
Something wrong?
– gimusi
Dec 3 '18 at 7:44
Something wrong?
– gimusi
Dec 3 '18 at 7:44
Something wrong?
– gimusi
Dec 3 '18 at 7:44
add a comment |
2
Are you familiar with the (standard and fundamental) limit $lim_{t to 0} frac{sin t}{t} = 1$?
– T. Bongers
Dec 2 '18 at 21:56