# Thread: Convergent or Divergent Series

1. ## Convergent or Divergent Series

For each of the series below select the letter from a to c that best applies and the letter from d to k that best applies. A possible answer is af, for example.

A. The series is absolutely convergent.
B. The series converges, but not absolutely.
C. The series diverges.
D. The alternating series test shows the series converges.
E. The series is a $$p$$-series.
F. The series is a geometric series.
G. We can decide whether this series converges by comparison with a $$p$$ series.
H. We can decide whether this series converges by comparison with a geometric series.
I. Partial sums of the series telescope.
J. The terms of the series do not have limit zero.
K. None of the above reasons applies to the convergence or divergence of the series.

f(n)=cos^2(npi)/(npi)
n from 1 to infinity

I know it is divergent by harmonic series, however CK is not the correct answer.

2. ## Re: Convergent or Divergent Series

Originally Posted by kjnabs
For each of the series below select the letter from a to c that best applies and the letter from d to k that best applies. A possible answer is af, for example.

A. The series is absolutely convergent.
B. The series converges, but not absolutely.
C. The series diverges.
D. The alternating series test shows the series converges.
E. The series is a $$p$$-series.
F. The series is a geometric series.
G. We can decide whether this series converges by comparison with a $$p$$ series.
H. We can decide whether this series converges by comparison with a geometric series.
I. Partial sums of the series telescope.
J. The terms of the series do not have limit zero.
K. None of the above reasons applies to the convergence or divergence of the series.
f(n)=cos^2(npi)/(npi)
n from 1 to infinity
I know it is divergent by harmonic series, however CK is not the correct answer.
I really do not know exactly how to read the above.

That said, the series $\displaystyle \sum\limits_{n = 1}^\infty {\frac{{{{\cos }^2}(n\pi )}}{{n\pi }}} = \sum\limits_{n = 1}^\infty {\frac{1}{{n\pi }}}$ diverges.

So the answer is C. The series diverges. Why do you doubt that answer?

3. ## Re: Convergent or Divergent Series

CG is the correct combination, the harmonic series is a p series with p = 1

4. ## Re: Convergent or Divergent Series

Originally Posted by agentmulder
CG is the correct combination, the harmonic series is a p series with p = 1
Frankly, if I were you I would get out of what ever course this come from.
Because, if you want to learn mathematics that kind of nonsense is going to handicap you.

5. ## Re: Convergent or Divergent Series

I only got partial marks on the problem and I was pretty sure that that was the question I was getting wrong, the other questions are as follow, I may have gotten one of them wrong

(2n+2)!/(n!)
^2
cos(npi)/(npi)
1/(n^(3/2))
1/(nlog(3+n))
(6+sin(n))/(n^(1/2))

I'm pretty sure the answers are as followed CJ, BD, AE, CK, CG,

6. ## Re: Convergent or Divergent Series

What is wrong with what i said?

7. ## Re: Convergent or Divergent Series

-Edit-

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