show that $lim _{nto infty }a_n:=:sqrt{a}$ [closed]











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







share|cite|improve this 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















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







share|cite|improve this 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













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







share|cite|improve this question
















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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 17 at 3:18









Chinnapparaj R

4,6081725




4,6081725










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














  • 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










1 Answer
1






active

oldest

votes

















up vote
0
down vote













If you are trying to use Newton method, just rewrite $$a_{n+1}=frac{1}{2} left(a_n+frac{a}{a_n}right)=a_n-frac{a_n^2-a}{2a_n}$$






share|cite|improve this answer




























    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 $$a_{n+1}=frac{1}{2} left(a_n+frac{a}{a_n}right)=a_n-frac{a_n^2-a}{2a_n}$$






    share|cite|improve this answer

























      up vote
      0
      down vote













      If you are trying to use Newton method, just rewrite $$a_{n+1}=frac{1}{2} left(a_n+frac{a}{a_n}right)=a_n-frac{a_n^2-a}{2a_n}$$






      share|cite|improve this answer























        up vote
        0
        down vote










        up vote
        0
        down vote









        If you are trying to use Newton method, just rewrite $$a_{n+1}=frac{1}{2} left(a_n+frac{a}{a_n}right)=a_n-frac{a_n^2-a}{2a_n}$$






        share|cite|improve this answer












        If you are trying to use Newton method, just rewrite $$a_{n+1}=frac{1}{2} left(a_n+frac{a}{a_n}right)=a_n-frac{a_n^2-a}{2a_n}$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 17 at 4:37









        Claude Leibovici

        116k1156131




        116k1156131















            -

            Popular posts from this blog

            Ellipse (mathématiques)

            Image
            Pour les articles homonymes, voir Ellipse. L'ellipse est le lieu des points dont la somme des distances à deux points fixes, dits foyers, est constante. Section du cône ou projection du cercle. En géométrie, une ellipse est une courbe plane fermée obtenue par l’intersection d’un cône de révolution avec un plan, à condition que celui-ci coupe l'axe de rotation du cône ou du cylindre : c'est une conique d'excentricité strictement comprise entre 0 et 1. On peut également la définir comme le lieu des points dont la somme des distances à deux points fixes, dits foyers, est constante (sa construction par la méthode du jardinier est très simple). Dans la vie courante, l’ellipse est la forme qu'on perçoit en regardant un cercle en perspective, ou la figure formée par l’ombre d'un disque sur une surface plane. On retrouve aussi, en première approximation [ 1 ] , des ellipses dans les trajectoires des corps célestes (planètes, comètes ou satellites arti...
            Read more

            Quarter-circle Tiles

            Image
            up vote 0 down vote favorite I have $99$ identical square tiles, each with a quarter-circle drawn on it like this: [asy] size(1.5cm); draw(Arc((2,0),1,90,180),red+1); draw((0,0)--(2,0)--(2,2)--(0,2)--(0,0)); [/asy] When I arrange the tiles in a $9times 11$ rectangular grid, each with a random orientation, what is the expected value of the number of full circles I form? I think this problem has to do with finding the chance any given 2x2 square has a circle, but I can't find it. expected-value share | cite | improve this question asked Nov 20 at 15:03 6minecraftninja 1 2 ...
            Read more

            Mont Emei

            Image
            Mont Emei.mw-parser-output .entete.map{background-image:url("//upload.wikimedia.org/wikipedia/commons/7/7a/Picto_infobox_map.png")} Vue du sommet Wanfo du mont Emei Géographie Altitude 3 099  m , Wanfo Coordonnées 29° 31′ 11″ nord, 103° 19′ 57″ est Administration Pays   Chine Province Sichuan Ville-préfecture Leshan Géolocalisation sur la carte : Sichuan Mont Emei Géolocalisation sur la carte : Chine Mont Emei modifier   Paysage panoramique du mont Emei, incluant le paysage panoramique du grand Bouddha de Leshan *   Patrimoine mondial de l'UNESCO Passerelle en bois sur le versant ouest Pays   Chine Subdivision Sichuan Type Mixte Critères (iv) (vi) (x) Superficie 15 400 ha Numéro d’identification 779 Zone géographique Asie et Pacifique  ** Année d’inscription 1996 (20 e session) * Descriptif officiel UNESCO ** Classification géog...
            Read more