Does the series with general term (2^n+1)/2^(n+1) converge?

[kdinser]

This is in the series and convergence chapter

infinit sum (2^(n)+1)/2^(n+1)

lim as n goes to infinity of
(2^(n)+1)/2^(n+1) = $$\frac{1+2^{-n}}{2}=1/2$$

couldn't get latex to work right for the first part.

 

[himanshu121]

$$Lim_{n \inf} {(\frac{1}{2})}^n = 0$$

 

[arildno]

You have:
$$\frac{2^{n}+1}{2^{n+1}}=\frac{1}{2}\frac{2^{n}+1}{2^{n}}=\frac{1}{2}(1+2^{-n})$$

 

[kdinser]

Thanks, my algebra still seems to be a little rusty.

forgot that $$2^{n+1}=2^n * 2^1$$

makes sense now and so do a few other ones that have been giving me headaches this morning.