How to use the squeeze theorem to show that $a_n→ 0$ as $n →∞ $ for the sequence $a_n :=1/n(1 +...
-1
Use the squeeze theorem to show that $a_n→ 0$ as $n →∞ $ for the sequence $a_n :=1/n(1 + n.cos^6(n^{2017} − 3√(5n))$.
What i did so far was i just try to use the fact that $0≤cos^6(t)≤1$ but i don't know how exactly.
real-analysis sequences-and-series
edited Nov 24 at 0:53
DonAntonio
176k1491225
asked Nov 23 at 13:32
Neels
227
add a comment |
-1
Use the squeeze theorem to show that $a_n→ 0$ as $n →∞ $ for the sequence $a_n :=1/n(1 + n.cos^6(n^{2017} − 3√(5n))$.
What i did so far was i just try to use the fact that $0≤cos^6(t)≤1$ but i don't know how exactly.
real-analysis sequences-and-series
edited Nov 24 at 0:53
DonAntonio
176k1491225
asked Nov 23 at 13:32
Neels
227
add a comment |
-1
-1
-1
1
Use the squeeze theorem to show that $a_n→ 0$ as $n →∞ $ for the sequence $a_n :=1/n(1 + n.cos^6(n^{2017} − 3√(5n))$.
What i did so far was i just try to use the fact that $0≤cos^6(t)≤1$ but i don't know how exactly.
real-analysis sequences-and-series
edited Nov 24 at 0:53
DonAntonio
176k1491225
asked Nov 23 at 13:32
Neels
227
Use the squeeze theorem to show that $a_n→ 0$ as $n →∞ $ for the sequence $a_n :=1/n(1 + n.cos^6(n^{2017} − 3√(5n))$.
What i did so far was i just try to use the fact that $0≤cos^6(t)≤1$ but i don't know how exactly.
real-analysis sequences-and-series
real-analysis sequences-and-series
edited Nov 24 at 0:53
DonAntonio
176k1491225
asked Nov 23 at 13:32
Neels
227
edited Nov 24 at 0:53
DonAntonio
176k1491225
asked Nov 23 at 13:32
Neels
227
edited Nov 24 at 0:53
DonAntonio
176k1491225
edited Nov 24 at 0:53
DonAntonio
176k1491225
edited Nov 24 at 0:53
DonAntonio
176k1491225
176k1491225
asked Nov 23 at 13:32
Neels
227
asked Nov 23 at 13:32
Neels
227
asked Nov 23 at 13:32
Neels
227
227
add a comment |
add a comment |
1 Answer
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$$frac1{n^2+n}=frac1{n(1+n)}lefrac1{nleft(1+ncos^6left(n^{2017}-3sqrt{5n}right)right)}lefrac1{n}$$
answered Nov 23 at 13:38
DonAntonio
176k1491225
@Nosrati Thanks, corrected. The basic idea remains.
– DonAntonio
Nov 23 at 13:49
The $(1+ ncos^6 dots )$ is upstairs isn't it?
– zhw.
Nov 23 at 21:03
@zhw. I'm not sure what you mean with upstairs, but int general $$1le1+ncos^6(...)le1+n$$
– DonAntonio
Nov 23 at 21:43
True, but as the problem is stated, that doesn't help.
– zhw.
Nov 23 at 23:39
@zhw. I think it does. Can you spot any mistake in what I did? If there's one I'll be glad to correct it, otherwise a straightforward use of the squeeze theorem solves the problem at once.
– DonAntonio
Nov 23 at 23:44
|
show 3 more comments
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1 Answer
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$$frac1{n^2+n}=frac1{n(1+n)}lefrac1{nleft(1+ncos^6left(n^{2017}-3sqrt{5n}right)right)}lefrac1{n}$$
answered Nov 23 at 13:38
DonAntonio
176k1491225
@Nosrati Thanks, corrected. The basic idea remains.
– DonAntonio
Nov 23 at 13:49
The $(1+ ncos^6 dots )$ is upstairs isn't it?
– zhw.
Nov 23 at 21:03
@zhw. I'm not sure what you mean with upstairs, but int general $$1le1+ncos^6(...)le1+n$$
– DonAntonio
Nov 23 at 21:43
True, but as the problem is stated, that doesn't help.
– zhw.
Nov 23 at 23:39
@zhw. I think it does. Can you spot any mistake in what I did? If there's one I'll be glad to correct it, otherwise a straightforward use of the squeeze theorem solves the problem at once.
– DonAntonio
Nov 23 at 23:44
|
show 3 more comments
2
$$frac1{n^2+n}=frac1{n(1+n)}lefrac1{nleft(1+ncos^6left(n^{2017}-3sqrt{5n}right)right)}lefrac1{n}$$
answered Nov 23 at 13:38
DonAntonio
176k1491225
@Nosrati Thanks, corrected. The basic idea remains.
– DonAntonio
Nov 23 at 13:49
The $(1+ ncos^6 dots )$ is upstairs isn't it?
– zhw.
Nov 23 at 21:03
@zhw. I'm not sure what you mean with upstairs, but int general $$1le1+ncos^6(...)le1+n$$
– DonAntonio
Nov 23 at 21:43
True, but as the problem is stated, that doesn't help.
– zhw.
Nov 23 at 23:39
@zhw. I think it does. Can you spot any mistake in what I did? If there's one I'll be glad to correct it, otherwise a straightforward use of the squeeze theorem solves the problem at once.
– DonAntonio
Nov 23 at 23:44
|
show 3 more comments
2
2
2
$$frac1{n^2+n}=frac1{n(1+n)}lefrac1{nleft(1+ncos^6left(n^{2017}-3sqrt{5n}right)right)}lefrac1{n}$$
answered Nov 23 at 13:38
DonAntonio
176k1491225
$$frac1{n^2+n}=frac1{n(1+n)}lefrac1{nleft(1+ncos^6left(n^{2017}-3sqrt{5n}right)right)}lefrac1{n}$$
answered Nov 23 at 13:38
DonAntonio
176k1491225
edited Nov 23 at 13:49
answered Nov 23 at 13:38
DonAntonio
176k1491225
answered Nov 23 at 13:38
DonAntonio
176k1491225
answered Nov 23 at 13:38
DonAntonio
176k1491225
176k1491225
@Nosrati Thanks, corrected. The basic idea remains.
– DonAntonio
Nov 23 at 13:49
The $(1+ ncos^6 dots )$ is upstairs isn't it?
– zhw.
Nov 23 at 21:03
@zhw. I'm not sure what you mean with upstairs, but int general $$1le1+ncos^6(...)le1+n$$
– DonAntonio
Nov 23 at 21:43
True, but as the problem is stated, that doesn't help.
– zhw.
Nov 23 at 23:39
@zhw. I think it does. Can you spot any mistake in what I did? If there's one I'll be glad to correct it, otherwise a straightforward use of the squeeze theorem solves the problem at once.
– DonAntonio
Nov 23 at 23:44
|
show 3 more comments
@Nosrati Thanks, corrected. The basic idea remains.
– DonAntonio
Nov 23 at 13:49
The $(1+ ncos^6 dots )$ is upstairs isn't it?
– zhw.
Nov 23 at 21:03
@zhw. I'm not sure what you mean with upstairs, but int general $$1le1+ncos^6(...)le1+n$$
– DonAntonio
Nov 23 at 21:43
True, but as the problem is stated, that doesn't help.
– zhw.
Nov 23 at 23:39
@zhw. I think it does. Can you spot any mistake in what I did? If there's one I'll be glad to correct it, otherwise a straightforward use of the squeeze theorem solves the problem at once.
– DonAntonio
Nov 23 at 23:44
@Nosrati Thanks, corrected. The basic idea remains.
– DonAntonio
Nov 23 at 13:49
@Nosrati Thanks, corrected. The basic idea remains.
– DonAntonio
Nov 23 at 13:49
The $(1+ ncos^6 dots )$ is upstairs isn't it?
– zhw.
Nov 23 at 21:03
The $(1+ ncos^6 dots )$ is upstairs isn't it?
– zhw.
Nov 23 at 21:03
@zhw. I'm not sure what you mean with upstairs, but int general $$1le1+ncos^6(...)le1+n$$
– DonAntonio
Nov 23 at 21:43
@zhw. I'm not sure what you mean with upstairs, but int general $$1le1+ncos^6(...)le1+n$$
– DonAntonio
Nov 23 at 21:43
True, but as the problem is stated, that doesn't help.
– zhw.
Nov 23 at 23:39
True, but as the problem is stated, that doesn't help.
– zhw.
Nov 23 at 23:39
@zhw. I think it does. Can you spot any mistake in what I did? If there's one I'll be glad to correct it, otherwise a straightforward use of the squeeze theorem solves the problem at once.
– DonAntonio
Nov 23 at 23:44
@zhw. I think it does. Can you spot any mistake in what I did? If there's one I'll be glad to correct it, otherwise a straightforward use of the squeeze theorem solves the problem at once.
– DonAntonio
Nov 23 at 23:44
|
show 3 more comments
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