Infinite Series Convergence using Comparison Test

[titasB]

Homework Statement

Determine whether the series is converging or diverging

Homework Equations

∞
∑ 1 / (3ⁿ +cos²(n))
n=1

The Attempt at a Solution

I used The Comparison Test, I'm just not sure I'm right. Here's what I've got:

The dominant term in the denominator is is 3ⁿ and
cos²(n) alternates between 0 and 1

so,

1 / (3ⁿ +cos²(n)) < 1 / 3ⁿ

which is convergent geometric series, since | r | = 1/3 < 1

And so, 1 / (3ⁿ +cos²(n)) is convergent according to the Comparison Test

 

[fourier jr]

looks ok to me. actually maybe you should change < to ≤ for when cos² is zero

 

[titasB]

Thanks. Wasn't sure about the cos²(n) part