How to find the Limit.
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0
down vote
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Given the following question first I thought I could use Caesaro's result somehow to solve this but it went nowhere.
Kindly help with this problem I am missing the correct approach.
Thanks and regards in advance
real-analysis sequences-and-series
asked Nov 15 at 16:41
Devendra Singh Rana
744216
add a comment |
up vote
0
down vote
favorite
Given the following question first I thought I could use Caesaro's result somehow to solve this but it went nowhere.
Kindly help with this problem I am missing the correct approach.
Thanks and regards in advance
real-analysis sequences-and-series
asked Nov 15 at 16:41
Devendra Singh Rana
744216
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Given the following question first I thought I could use Caesaro's result somehow to solve this but it went nowhere.
Kindly help with this problem I am missing the correct approach.
Thanks and regards in advance
real-analysis sequences-and-series
asked Nov 15 at 16:41
Devendra Singh Rana
744216
Given the following question first I thought I could use Caesaro's result somehow to solve this but it went nowhere.
Kindly help with this problem I am missing the correct approach.
Thanks and regards in advance
real-analysis sequences-and-series
real-analysis sequences-and-series
asked Nov 15 at 16:41
Devendra Singh Rana
744216
asked Nov 15 at 16:41
Devendra Singh Rana
744216
asked Nov 15 at 16:41
Devendra Singh Rana
744216
asked Nov 15 at 16:41
Devendra Singh Rana
744216
asked Nov 15 at 16:41
Devendra Singh Rana
744216
744216
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
up vote
2
down vote
accepted
HINT
By Stolz–Cesàro theorem we have
$$lim_{nto infty} frac{sum_{i=1}^n a_ix_i}{s_n}=lim_{nto infty} frac{ sum_{i=1}^{n+1} a_ix_i-sum_{i=1}^n a_ix_i}{s_{n+1}-s_n}$$
when the RHS exists.
answered Nov 15 at 17:12
gimusi
87.2k74393
I am not aware of this theorem@gimusi any links will be helpful.
– Devendra Singh Rana
Nov 15 at 17:17
1
@DevendraSinghRana I've added a reference for that theorem.
– gimusi
Nov 15 at 17:22
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
HINT
By Stolz–Cesàro theorem we have
$$lim_{nto infty} frac{sum_{i=1}^n a_ix_i}{s_n}=lim_{nto infty} frac{ sum_{i=1}^{n+1} a_ix_i-sum_{i=1}^n a_ix_i}{s_{n+1}-s_n}$$
when the RHS exists.
answered Nov 15 at 17:12
gimusi
87.2k74393
I am not aware of this theorem@gimusi any links will be helpful.
– Devendra Singh Rana
Nov 15 at 17:17
1
@DevendraSinghRana I've added a reference for that theorem.
– gimusi
Nov 15 at 17:22
add a comment |
up vote
2
down vote
accepted
HINT
By Stolz–Cesàro theorem we have
$$lim_{nto infty} frac{sum_{i=1}^n a_ix_i}{s_n}=lim_{nto infty} frac{ sum_{i=1}^{n+1} a_ix_i-sum_{i=1}^n a_ix_i}{s_{n+1}-s_n}$$
when the RHS exists.
answered Nov 15 at 17:12
gimusi
87.2k74393
I am not aware of this theorem@gimusi any links will be helpful.
– Devendra Singh Rana
Nov 15 at 17:17
1
@DevendraSinghRana I've added a reference for that theorem.
– gimusi
Nov 15 at 17:22
add a comment |
up vote
2
down vote
accepted
up vote
2
down vote
accepted
HINT
By Stolz–Cesàro theorem we have
$$lim_{nto infty} frac{sum_{i=1}^n a_ix_i}{s_n}=lim_{nto infty} frac{ sum_{i=1}^{n+1} a_ix_i-sum_{i=1}^n a_ix_i}{s_{n+1}-s_n}$$
when the RHS exists.
answered Nov 15 at 17:12
gimusi
87.2k74393
HINT
By Stolz–Cesàro theorem we have
$$lim_{nto infty} frac{sum_{i=1}^n a_ix_i}{s_n}=lim_{nto infty} frac{ sum_{i=1}^{n+1} a_ix_i-sum_{i=1}^n a_ix_i}{s_{n+1}-s_n}$$
when the RHS exists.
answered Nov 15 at 17:12
gimusi
87.2k74393
edited Nov 15 at 17:21
answered Nov 15 at 17:12
gimusi
87.2k74393
answered Nov 15 at 17:12
gimusi
87.2k74393
answered Nov 15 at 17:12
gimusi
87.2k74393
87.2k74393
I am not aware of this theorem@gimusi any links will be helpful.
– Devendra Singh Rana
Nov 15 at 17:17
1
@DevendraSinghRana I've added a reference for that theorem.
– gimusi
Nov 15 at 17:22
add a comment |
I am not aware of this theorem@gimusi any links will be helpful.
– Devendra Singh Rana
Nov 15 at 17:17
1
@DevendraSinghRana I've added a reference for that theorem.
– gimusi
Nov 15 at 17:22
I am not aware of this theorem@gimusi any links will be helpful.
– Devendra Singh Rana
Nov 15 at 17:17
I am not aware of this theorem@gimusi any links will be helpful.
– Devendra Singh Rana
Nov 15 at 17:17
1
1
@DevendraSinghRana I've added a reference for that theorem.
– gimusi
Nov 15 at 17:22
@DevendraSinghRana I've added a reference for that theorem.
– gimusi
Nov 15 at 17:22
add a comment |
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