how to find the asymptotic growth of f
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The question is:
Let $$S_n=left{tinmathbb{N}mid ttext{ does not contain }ntext{ consectuive }4'text{s}right}$$ E.g. $2464in S_2$, but $2544$ is not.
Let $$f(n)=sum_{sin S_n}frac{1}{s}$$
Prove that $f(n)$ is finite and find the asymptotic growth of $f$.
I have tried to find out the number of $d$-digit numbers in $S_2$ for any integer $d$. Then approximate the value of the inverse of all these $d$-digit numbers in $S_2$. Then generalize the number of $d$-digit numbers in $S_n$ for any integer $d,n$.
I find it hard to find the number of $d$-digit numbers in $S_3$ for any integer $d$. Because $S_3$ allows the numbers to have two places having $2$ consecutive $4$'s, like $44544,544344$ and $4454$ is also in $S_3$.
Then I run out of ideas. How can I do this question?
summation permutations asymptotics infinity
asked Nov 25 at 14:02
idunno
71
add a comment |
up vote
-1
down vote
favorite
The question is:
Let $$S_n=left{tinmathbb{N}mid ttext{ does not contain }ntext{ consectuive }4'text{s}right}$$ E.g. $2464in S_2$, but $2544$ is not.
Let $$f(n)=sum_{sin S_n}frac{1}{s}$$
Prove that $f(n)$ is finite and find the asymptotic growth of $f$.
I have tried to find out the number of $d$-digit numbers in $S_2$ for any integer $d$. Then approximate the value of the inverse of all these $d$-digit numbers in $S_2$. Then generalize the number of $d$-digit numbers in $S_n$ for any integer $d,n$.
I find it hard to find the number of $d$-digit numbers in $S_3$ for any integer $d$. Because $S_3$ allows the numbers to have two places having $2$ consecutive $4$'s, like $44544,544344$ and $4454$ is also in $S_3$.
Then I run out of ideas. How can I do this question?
summation permutations asymptotics infinity
asked Nov 25 at 14:02
idunno
71
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 25 at 14:15
add a comment |
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
The question is:
Let $$S_n=left{tinmathbb{N}mid ttext{ does not contain }ntext{ consectuive }4'text{s}right}$$ E.g. $2464in S_2$, but $2544$ is not.
Let $$f(n)=sum_{sin S_n}frac{1}{s}$$
Prove that $f(n)$ is finite and find the asymptotic growth of $f$.
I have tried to find out the number of $d$-digit numbers in $S_2$ for any integer $d$. Then approximate the value of the inverse of all these $d$-digit numbers in $S_2$. Then generalize the number of $d$-digit numbers in $S_n$ for any integer $d,n$.
I find it hard to find the number of $d$-digit numbers in $S_3$ for any integer $d$. Because $S_3$ allows the numbers to have two places having $2$ consecutive $4$'s, like $44544,544344$ and $4454$ is also in $S_3$.
Then I run out of ideas. How can I do this question?
summation permutations asymptotics infinity
asked Nov 25 at 14:02
idunno
71
The question is:
Let $$S_n=left{tinmathbb{N}mid ttext{ does not contain }ntext{ consectuive }4'text{s}right}$$ E.g. $2464in S_2$, but $2544$ is not.
Let $$f(n)=sum_{sin S_n}frac{1}{s}$$
Prove that $f(n)$ is finite and find the asymptotic growth of $f$.
I have tried to find out the number of $d$-digit numbers in $S_2$ for any integer $d$. Then approximate the value of the inverse of all these $d$-digit numbers in $S_2$. Then generalize the number of $d$-digit numbers in $S_n$ for any integer $d,n$.
I find it hard to find the number of $d$-digit numbers in $S_3$ for any integer $d$. Because $S_3$ allows the numbers to have two places having $2$ consecutive $4$'s, like $44544,544344$ and $4454$ is also in $S_3$.
Then I run out of ideas. How can I do this question?
summation permutations asymptotics infinity
summation permutations asymptotics infinity
asked Nov 25 at 14:02
idunno
71
asked Nov 25 at 14:02
idunno
71
edited Nov 25 at 14:26
asked Nov 25 at 14:02
idunno
71
asked Nov 25 at 14:02
idunno
71
asked Nov 25 at 14:02
idunno
71
71
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 25 at 14:15
add a comment |
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 25 at 14:15
1
1
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 25 at 14:15
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 25 at 14:15
add a comment |
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Nov 25 at 14:15