Limit calue -- HELP!

[wartburg]

Limit value -- HELP!

Dear All,

I need your help for the limit value of the following progression:

[(9*n-2)/(9*n+5)]^(2*n-4)

First I divided both counter and denominator by "n" getting the limit value of the whole fraction "1". But it should be incorrect, as the real (Excel) function tends somewhere to 0.22XXX.
Could you give me the right solution?
Thanks

 

[pka]

Dear All,

I need your help for the limit value of the following progression:

[(9*n-2)/(9*n+5)]^(2*n-4)

Have a look at this.

Then apply this \(\displaystyle {\lim _{n \to \infty }}{\left( {1 + \frac{{a}}{{bn + c}}} \right)^{dn + p}} = {e^{\dfrac{{ad}}{b}}}\)

 

[Deleted member 4993]

Dear All,

I need your help for the limit value of the following progression:

[(9*n-2)/(9*n+5)]^(2*n-4)

First I divided both counter and denominator by "n" getting the limit value of the whole fraction "1". But it should be incorrect, as the real (Excel) function tends somewhere to 0.22XXX.
Could you give me the right solution?
Thanks

Do you know the following limit:

\(\displaystyle \displaystyle \lim_{n \to \infty}\left [1 + \frac{x}{n}\right ]^n \ = \ ?\)

 

[wartburg]

Have a look at this.

Then apply this \(\displaystyle {\lim _{n \to \infty }}{\left( {1 + \frac{{a}}{{bn + c}}} \right)^{dn + p}} = {e^{\dfrac{{ad}}{b}}}\)

That's it!
Thanks a lot!

 

[HallsofIvy]

That is, of course, an extension of Subhotosh Kahn's limit.