Recursive square root inside square root problem
Clash Royale CLAN TAG#URR8PPP
up vote
3
down vote
favorite
I have been debating this issue for days:
I can't find a recursive function of this equation:
$largesqrt2+pi sqrt3+pisqrt4+pisqrt5+dotsb$
has been trying to find a solution this for days now, is what I have achieved so far:
$f(n)=sqrt2 f(n-1), f(1)=sqrt2$
Unfortunately, I do not know how to move forward,
thanks a lot!
sequences-and-series recurrence-relations recursion nested-radicals
asked Sep 3 at 7:51
Gionata Donati
162
add a comment |Â
up vote
3
down vote
favorite
I have been debating this issue for days:
I can't find a recursive function of this equation:
$largesqrt2+pi sqrt3+pisqrt4+pisqrt5+dotsb$
has been trying to find a solution this for days now, is what I have achieved so far:
$f(n)=sqrt2 f(n-1), f(1)=sqrt2$
Unfortunately, I do not know how to move forward,
thanks a lot!
sequences-and-series recurrence-relations recursion nested-radicals
asked Sep 3 at 7:51
Gionata Donati
162
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I have been debating this issue for days:
I can't find a recursive function of this equation:
$largesqrt2+pi sqrt3+pisqrt4+pisqrt5+dotsb$
has been trying to find a solution this for days now, is what I have achieved so far:
$f(n)=sqrt2 f(n-1), f(1)=sqrt2$
Unfortunately, I do not know how to move forward,
thanks a lot!
sequences-and-series recurrence-relations recursion nested-radicals
asked Sep 3 at 7:51
Gionata Donati
162
I have been debating this issue for days:
I can't find a recursive function of this equation:
$largesqrt2+pi sqrt3+pisqrt4+pisqrt5+dotsb$
has been trying to find a solution this for days now, is what I have achieved so far:
$f(n)=sqrt2 f(n-1), f(1)=sqrt2$
Unfortunately, I do not know how to move forward,
thanks a lot!
sequences-and-series recurrence-relations recursion nested-radicals
sequences-and-series recurrence-relations recursion nested-radicals
asked Sep 3 at 7:51
Gionata Donati
162
asked Sep 3 at 7:51
Gionata Donati
162
asked Sep 3 at 7:51
Gionata Donati
162
asked Sep 3 at 7:51
Gionata Donati
162
asked Sep 3 at 7:51
Gionata Donati
162
162
add a comment |Â
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
1
down vote
I would write it as
$$
fleft(nright)=sqrtn+1+pi fleft(n+1right),
$$
Hence
$$
fleft(1right)=sqrt2+pi fleft(2right), fleft(2right)=sqrt3+pi fleft(3right) Rightarrow fleft(1right)=sqrt2+pisqrt3+fleft(3right)
$$
which means you search for $fleft(1right)$.
$$
fleft(n+1right)=frac1pileft(fleft(nright)^2-n-1right)
$$
answered Sep 3 at 8:42
Atmos
4,741119
I dont think so, wolfram interprets it as f(0)=0
– Atmos
Sep 3 at 9:51
I don t think so. However do you want to find a value to this ?
– Atmos
Sep 3 at 15:21
There is no value for n=0 the sequence i wrote us for n>=1
– Atmos
Sep 3 at 15:30
1
Hi, thank you for your reply. It is not correct, both in Matlab and WolframAlpha the sequence is not correct. link If someone can understand how to correct your formula would be perfect, yesterday I tried but I failed
– Gionata Donati
Sep 4 at 8:38
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
I would write it as
$$
fleft(nright)=sqrtn+1+pi fleft(n+1right),
$$
Hence
$$
fleft(1right)=sqrt2+pi fleft(2right), fleft(2right)=sqrt3+pi fleft(3right) Rightarrow fleft(1right)=sqrt2+pisqrt3+fleft(3right)
$$
which means you search for $fleft(1right)$.
$$
fleft(n+1right)=frac1pileft(fleft(nright)^2-n-1right)
$$
answered Sep 3 at 8:42
Atmos
4,741119
I dont think so, wolfram interprets it as f(0)=0
– Atmos
Sep 3 at 9:51
I don t think so. However do you want to find a value to this ?
– Atmos
Sep 3 at 15:21
There is no value for n=0 the sequence i wrote us for n>=1
– Atmos
Sep 3 at 15:30
1
Hi, thank you for your reply. It is not correct, both in Matlab and WolframAlpha the sequence is not correct. link If someone can understand how to correct your formula would be perfect, yesterday I tried but I failed
– Gionata Donati
Sep 4 at 8:38
add a comment |Â
up vote
1
down vote
I would write it as
$$
fleft(nright)=sqrtn+1+pi fleft(n+1right),
$$
Hence
$$
fleft(1right)=sqrt2+pi fleft(2right), fleft(2right)=sqrt3+pi fleft(3right) Rightarrow fleft(1right)=sqrt2+pisqrt3+fleft(3right)
$$
which means you search for $fleft(1right)$.
$$
fleft(n+1right)=frac1pileft(fleft(nright)^2-n-1right)
$$
answered Sep 3 at 8:42
Atmos
4,741119
I dont think so, wolfram interprets it as f(0)=0
– Atmos
Sep 3 at 9:51
I don t think so. However do you want to find a value to this ?
– Atmos
Sep 3 at 15:21
There is no value for n=0 the sequence i wrote us for n>=1
– Atmos
Sep 3 at 15:30
1
Hi, thank you for your reply. It is not correct, both in Matlab and WolframAlpha the sequence is not correct. link If someone can understand how to correct your formula would be perfect, yesterday I tried but I failed
– Gionata Donati
Sep 4 at 8:38
add a comment |Â
up vote
1
down vote
up vote
1
down vote
I would write it as
$$
fleft(nright)=sqrtn+1+pi fleft(n+1right),
$$
Hence
$$
fleft(1right)=sqrt2+pi fleft(2right), fleft(2right)=sqrt3+pi fleft(3right) Rightarrow fleft(1right)=sqrt2+pisqrt3+fleft(3right)
$$
which means you search for $fleft(1right)$.
$$
fleft(n+1right)=frac1pileft(fleft(nright)^2-n-1right)
$$
answered Sep 3 at 8:42
Atmos
4,741119
I would write it as
$$
fleft(nright)=sqrtn+1+pi fleft(n+1right),
$$
Hence
$$
fleft(1right)=sqrt2+pi fleft(2right), fleft(2right)=sqrt3+pi fleft(3right) Rightarrow fleft(1right)=sqrt2+pisqrt3+fleft(3right)
$$
which means you search for $fleft(1right)$.
$$
fleft(n+1right)=frac1pileft(fleft(nright)^2-n-1right)
$$
answered Sep 3 at 8:42
Atmos
4,741119
answered Sep 3 at 8:42
Atmos
4,741119
answered Sep 3 at 8:42
Atmos
4,741119
answered Sep 3 at 8:42
Atmos
4,741119
4,741119
I dont think so, wolfram interprets it as f(0)=0
– Atmos
Sep 3 at 9:51
I don t think so. However do you want to find a value to this ?
– Atmos
Sep 3 at 15:21
There is no value for n=0 the sequence i wrote us for n>=1
– Atmos
Sep 3 at 15:30
1
Hi, thank you for your reply. It is not correct, both in Matlab and WolframAlpha the sequence is not correct. link If someone can understand how to correct your formula would be perfect, yesterday I tried but I failed
– Gionata Donati
Sep 4 at 8:38
add a comment |Â
I dont think so, wolfram interprets it as f(0)=0
– Atmos
Sep 3 at 9:51
I don t think so. However do you want to find a value to this ?
– Atmos
Sep 3 at 15:21
There is no value for n=0 the sequence i wrote us for n>=1
– Atmos
Sep 3 at 15:30
1
Hi, thank you for your reply. It is not correct, both in Matlab and WolframAlpha the sequence is not correct. link If someone can understand how to correct your formula would be perfect, yesterday I tried but I failed
– Gionata Donati
Sep 4 at 8:38
I dont think so, wolfram interprets it as f(0)=0
– Atmos
Sep 3 at 9:51
I dont think so, wolfram interprets it as f(0)=0
– Atmos
Sep 3 at 9:51
I don t think so. However do you want to find a value to this ?
– Atmos
Sep 3 at 15:21
I don t think so. However do you want to find a value to this ?
– Atmos
Sep 3 at 15:21
There is no value for n=0 the sequence i wrote us for n>=1
– Atmos
Sep 3 at 15:30
There is no value for n=0 the sequence i wrote us for n>=1
– Atmos
Sep 3 at 15:30
1
1
Hi, thank you for your reply. It is not correct, both in Matlab and WolframAlpha the sequence is not correct. link If someone can understand how to correct your formula would be perfect, yesterday I tried but I failed
– Gionata Donati
Sep 4 at 8:38
Hi, thank you for your reply. It is not correct, both in Matlab and WolframAlpha the sequence is not correct. link If someone can understand how to correct your formula would be perfect, yesterday I tried but I failed
– Gionata Donati
Sep 4 at 8:38
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2903628%2frecursive-square-root-inside-square-root-problem%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
