convergence

[hine0200]

How do i know if the sequence e^n/3^n converges or diverges?? How would i start the problem?

 

[JeffM]

Does the series a[sup:4utcrpzx]n[/sup:4utcrpzx] ever converge?

Under what conditions?

 

[hine0200]

doesn't it converge if a is between 0 and 1?

 

[JeffM]

doesn't it converge if a is between 0 and 1? Almost right. It converges if |a| < 1 Consequently, it also converges if 0 <= a < 1.

Now do you see any possible relationship between the expression (e[sup:33vvmes9]n[/sup:33vvmes9] / 3[sup:33vvmes9]n[/sup:33vvmes9]) and the expression a[sup:33vvmes9]n[/sup:33vvmes9]?