Question

convergence, divergence help please!!
is the series convergent or divergent?
a_n=(-1)^n+1*1/4^n

Answer 1

alternating series test solves this problem.

Answer 2

so if the limit =o, series converges.....

Answer 3

It converges since the terms decrease monotonically to 0 as n grows large.

Answer 4

but how do I show that with a limit statement?

Answer 5

I have it in my head that you can't do the limits with the exponent equaling infinity

Answer 6

is this the term of the series \[a_n= \frac{(-1)^n}{4^n}\]

Answer 7

looks good

Answer 8

the equation images are not showing up for some reason
I can't tell what you have done... Ill try refreshing

Answer 9

no sorry, the numerator is exponent n+1

Answer 10

it wont let me put (n+1) into the equation editor

Answer 11

(-1)^{n+1}/4^{n} < 1/2^{n}
we know that the left hand side converges b/c the right hand side converges. The proof of 1/2^{n} convergent is contained in many text books.