show that $lim _{nto infty }a_n:=:sqrt{a}$ [closed]
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Suppose $a_1 = c$ and $a,c>0$ and $$a_{n+1}=frac{1}{2}cdot left(a_n+frac{a}{a_n}right)$$
Show that $lim _{nto infty }a_n:=:sqrt{a}$
sequences-and-series
edited Nov 17 at 3:18
Chinnapparaj R
4,6081725
asked Nov 16 at 23:31
Bashar
43
closed as off-topic by Servaes, Cesareo, max_zorn, José Carlos Santos, Scientifica Nov 17 at 12:49
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." – Servaes, Cesareo, max_zorn, José Carlos Santos, Scientifica
If this question can be reworded to fit the rules in the help center, please edit the question.
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up vote
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down vote
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Suppose $a_1 = c$ and $a,c>0$ and $$a_{n+1}=frac{1}{2}cdot left(a_n+frac{a}{a_n}right)$$
Show that $lim _{nto infty }a_n:=:sqrt{a}$
sequences-and-series
edited Nov 17 at 3:18
Chinnapparaj R
4,6081725
asked Nov 16 at 23:31
Bashar
43
closed as off-topic by Servaes, Cesareo, max_zorn, José Carlos Santos, Scientifica Nov 17 at 12:49
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." – Servaes, Cesareo, max_zorn, José Carlos Santos, Scientifica
If this question can be reworded to fit the rules in the help center, please edit the question.
5
So what have you tried?
– user3482749
Nov 16 at 23:34
Check this: math.stackexchange.com/questions/1155610/…
– NoChance
Nov 16 at 23:42
i'm trying to use Newton–Raphson method
– Bashar
Nov 16 at 23:43
See 2.1 here: math.mit.edu/~stevenj/18.335/newton-sqrt.pdf
– NoChance
Nov 16 at 23:55
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Suppose $a_1 = c$ and $a,c>0$ and $$a_{n+1}=frac{1}{2}cdot left(a_n+frac{a}{a_n}right)$$
Show that $lim _{nto infty }a_n:=:sqrt{a}$
sequences-and-series
edited Nov 17 at 3:18
Chinnapparaj R
4,6081725
asked Nov 16 at 23:31
Bashar
43
Suppose $a_1 = c$ and $a,c>0$ and $$a_{n+1}=frac{1}{2}cdot left(a_n+frac{a}{a_n}right)$$
Show that $lim _{nto infty }a_n:=:sqrt{a}$
sequences-and-series
sequences-and-series
edited Nov 17 at 3:18
Chinnapparaj R
4,6081725
asked Nov 16 at 23:31
Bashar
43
edited Nov 17 at 3:18
Chinnapparaj R
4,6081725
asked Nov 16 at 23:31
Bashar
43
edited Nov 17 at 3:18
Chinnapparaj R
4,6081725
edited Nov 17 at 3:18
Chinnapparaj R
4,6081725
edited Nov 17 at 3:18
Chinnapparaj R
4,6081725
4,6081725
asked Nov 16 at 23:31
Bashar
43
asked Nov 16 at 23:31
Bashar
43
asked Nov 16 at 23:31
Bashar
43
43
closed as off-topic by Servaes, Cesareo, max_zorn, José Carlos Santos, Scientifica Nov 17 at 12:49
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." – Servaes, Cesareo, max_zorn, José Carlos Santos, Scientifica
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Servaes, Cesareo, max_zorn, José Carlos Santos, Scientifica Nov 17 at 12:49
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." – Servaes, Cesareo, max_zorn, José Carlos Santos, Scientifica
If this question can be reworded to fit the rules in the help center, please edit the question.
5
So what have you tried?
– user3482749
Nov 16 at 23:34
Check this: math.stackexchange.com/questions/1155610/…
– NoChance
Nov 16 at 23:42
i'm trying to use Newton–Raphson method
– Bashar
Nov 16 at 23:43
See 2.1 here: math.mit.edu/~stevenj/18.335/newton-sqrt.pdf
– NoChance
Nov 16 at 23:55
add a comment |
5
So what have you tried?
– user3482749
Nov 16 at 23:34
Check this: math.stackexchange.com/questions/1155610/…
– NoChance
Nov 16 at 23:42
i'm trying to use Newton–Raphson method
– Bashar
Nov 16 at 23:43
See 2.1 here: math.mit.edu/~stevenj/18.335/newton-sqrt.pdf
– NoChance
Nov 16 at 23:55
5
5
So what have you tried?
– user3482749
Nov 16 at 23:34
So what have you tried?
– user3482749
Nov 16 at 23:34
Check this: math.stackexchange.com/questions/1155610/…
– NoChance
Nov 16 at 23:42
Check this: math.stackexchange.com/questions/1155610/…
– NoChance
Nov 16 at 23:42
i'm trying to use Newton–Raphson method
– Bashar
Nov 16 at 23:43
i'm trying to use Newton–Raphson method
– Bashar
Nov 16 at 23:43
See 2.1 here: math.mit.edu/~stevenj/18.335/newton-sqrt.pdf
– NoChance
Nov 16 at 23:55
See 2.1 here: math.mit.edu/~stevenj/18.335/newton-sqrt.pdf
– NoChance
Nov 16 at 23:55
add a comment |
1 Answer
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If you are trying to use Newton method, just rewrite $$a_{n+1}=frac{1}{2} left(a_n+frac{a}{a_n}right)=a_n-frac{a_n^2-a}{2a_n}$$
answered Nov 17 at 4:37
Claude Leibovici
116k1156131
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
If you are trying to use Newton method, just rewrite $$a_{n+1}=frac{1}{2} left(a_n+frac{a}{a_n}right)=a_n-frac{a_n^2-a}{2a_n}$$
answered Nov 17 at 4:37
Claude Leibovici
116k1156131
add a comment |
up vote
0
down vote
If you are trying to use Newton method, just rewrite $$a_{n+1}=frac{1}{2} left(a_n+frac{a}{a_n}right)=a_n-frac{a_n^2-a}{2a_n}$$
answered Nov 17 at 4:37
Claude Leibovici
116k1156131
add a comment |
up vote
0
down vote
up vote
0
down vote
If you are trying to use Newton method, just rewrite $$a_{n+1}=frac{1}{2} left(a_n+frac{a}{a_n}right)=a_n-frac{a_n^2-a}{2a_n}$$
answered Nov 17 at 4:37
Claude Leibovici
116k1156131
If you are trying to use Newton method, just rewrite $$a_{n+1}=frac{1}{2} left(a_n+frac{a}{a_n}right)=a_n-frac{a_n^2-a}{2a_n}$$
answered Nov 17 at 4:37
Claude Leibovici
116k1156131
answered Nov 17 at 4:37
Claude Leibovici
116k1156131
answered Nov 17 at 4:37
Claude Leibovici
116k1156131
answered Nov 17 at 4:37
Claude Leibovici
116k1156131
116k1156131
add a comment |
add a comment |
5
So what have you tried?
– user3482749
Nov 16 at 23:34
Check this: math.stackexchange.com/questions/1155610/…
– NoChance
Nov 16 at 23:42
i'm trying to use Newton–Raphson method
– Bashar
Nov 16 at 23:43
See 2.1 here: math.mit.edu/~stevenj/18.335/newton-sqrt.pdf
– NoChance
Nov 16 at 23:55