$nin N, a_{n+1} = a_n (1 - a_n)$ , $0 < a_0 < 1$. Prove that $limlimits_{ntoinfty} a_ncdot n = 1$.
$begingroup$
$nin N, a_{n+1} = a_n (1 - a_n)$ , $0 < a_0 < 1$. Prove that $limlimits_{ntoinfty} a_ncdot n = 1$. I proved that $limlimits_{ntoinfty} a_n = 0$ and that $a_n$ is strictly decreasing. I tried Cezaro Stolz but didn't get anywhere. Thanks in advance.
calculus sequences-and-series limits
edited Jan 25 at 23:23
rtybase
11.4k31533
asked Jan 25 at 17:26
Claudiu BbnClaudiu Bbn
968
$endgroup$
add a comment |
$begingroup$
$nin N, a_{n+1} = a_n (1 - a_n)$ , $0 < a_0 < 1$. Prove that $limlimits_{ntoinfty} a_ncdot n = 1$. I proved that $limlimits_{ntoinfty} a_n = 0$ and that $a_n$ is strictly decreasing. I tried Cezaro Stolz but didn't get anywhere. Thanks in advance.
calculus sequences-and-series limits
edited Jan 25 at 23:23
rtybase
11.4k31533
asked Jan 25 at 17:26
Claudiu BbnClaudiu Bbn
968
$endgroup$
add a comment |
$begingroup$
$nin N, a_{n+1} = a_n (1 - a_n)$ , $0 < a_0 < 1$. Prove that $limlimits_{ntoinfty} a_ncdot n = 1$. I proved that $limlimits_{ntoinfty} a_n = 0$ and that $a_n$ is strictly decreasing. I tried Cezaro Stolz but didn't get anywhere. Thanks in advance.
calculus sequences-and-series limits
edited Jan 25 at 23:23
rtybase
11.4k31533
asked Jan 25 at 17:26
Claudiu BbnClaudiu Bbn
968
$endgroup$
$nin N, a_{n+1} = a_n (1 - a_n)$ , $0 < a_0 < 1$. Prove that $limlimits_{ntoinfty} a_ncdot n = 1$. I proved that $limlimits_{ntoinfty} a_n = 0$ and that $a_n$ is strictly decreasing. I tried Cezaro Stolz but didn't get anywhere. Thanks in advance.
calculus sequences-and-series limits
calculus sequences-and-series limits
edited Jan 25 at 23:23
rtybase
11.4k31533
asked Jan 25 at 17:26
Claudiu BbnClaudiu Bbn
968
edited Jan 25 at 23:23
rtybase
11.4k31533
asked Jan 25 at 17:26
Claudiu BbnClaudiu Bbn
968
edited Jan 25 at 23:23
rtybase
11.4k31533
edited Jan 25 at 23:23
rtybase
11.4k31533
edited Jan 25 at 23:23
rtybase
11.4k31533
11.4k31533
asked Jan 25 at 17:26
Claudiu BbnClaudiu Bbn
968
asked Jan 25 at 17:26
Claudiu BbnClaudiu Bbn
968
asked Jan 25 at 17:26
Claudiu BbnClaudiu Bbn
968
968
add a comment |
add a comment |
1 Answer
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$begingroup$
Prove that $frac{1}{a_{n+1}}-frac{1}{a_n} rightarrow 1$.
answered Jan 25 at 17:29
MindlackMindlack
4,920211
$endgroup$
add a comment |
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$begingroup$
Prove that $frac{1}{a_{n+1}}-frac{1}{a_n} rightarrow 1$.
answered Jan 25 at 17:29
MindlackMindlack
4,920211
$endgroup$
add a comment |
$begingroup$
Prove that $frac{1}{a_{n+1}}-frac{1}{a_n} rightarrow 1$.
answered Jan 25 at 17:29
MindlackMindlack
4,920211
$endgroup$
add a comment |
$begingroup$
Prove that $frac{1}{a_{n+1}}-frac{1}{a_n} rightarrow 1$.
answered Jan 25 at 17:29
MindlackMindlack
4,920211
$endgroup$
Prove that $frac{1}{a_{n+1}}-frac{1}{a_n} rightarrow 1$.
answered Jan 25 at 17:29
MindlackMindlack
4,920211
answered Jan 25 at 17:29
MindlackMindlack
4,920211
answered Jan 25 at 17:29
MindlackMindlack
4,920211
answered Jan 25 at 17:29
MindlackMindlack
4,920211
4,920211
add a comment |
add a comment |
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