Can't solve a sequence (to determine if a given value is a member)

[theakdad]

I would think the argument I gave in my post previous to this would suffice then.

I agree...

But,now i have new problem,about Mathematical induction,should i open new Thread?

 

[MarkFL]

I agree...

But,now i have new problem,about Mathematical induction,should i open new Thread?

Yes, and I would post it in our Discrete Mathematics sub-forum.

 

[theakdad]

Yes, and I would post it in our Discrete Mathematics sub-forum.

I will...

Maybe you can take a look...if you want...

 

[theakdad]

I still have one question...What kind of type this sequence is? Arithmetic or geometric? I can't figure it out...

 

[MarkFL]

I still have one question...What kind of type this sequence is? Arithmetic or geometric? I can't figure it out...

An arithmetic sequence has the property:

$$a_{n+1}-a_{n}=d$$

While a geometric sequence would have the property:

$$\frac{a_{n+1}}{a_{n}}=r$$

Note: Both $d$ and $r$ are constants that do not depend on $n$. Does this sequence satisfy either property?

 

[theakdad]

An arithmetic sequence has the property:

$$a_{n+1}-a_{n}=d$$

While a geometric sequence would have the property:

$$\frac{a_{n+1}}{a_{n}}=r$$

Note: Both $d$ and $r$ are constants that do not depend on $n$. Does this sequence satisfy either property?

It seems its arthmetic

 

[MarkFL]

It seems its arthmetic

I find:

$$a_{n+1}-a_{n}=\frac{(n+1)^2+1}{2(n+1)^2}-\frac{n^2+1}{2n^2}=-\frac{2n+1}{2n^2(n+1)^2}$$

Thus, the difference between two succeeding terms is a function of $n$, and so the sequence is not arithmetic.

 

[theakdad]

I find:

$$a_{n+1}-a_{n}=\frac{(n+1)^2+1}{2(n+1)^2}-\frac{n^2+1}{2n^2}=-\frac{2n+1}{2n^2(n+1)^2}$$

Thus, the difference between two succeeding terms is a function of $n$, and so the sequence is not arithmetic.

Ad its not geometric?

 

[MarkFL]

And its not geometric?

What do you find when you compute the ratio I gave above?

 

[theakdad]

What do you find when you compute the ratio I gave above?

Will try tomorrow,im litlle busy now