Absolute convergence

**chizmin10** · October 2nd 2012, 06:43 PM

Determine whether the series (-1)^k-11/k+K^1/2 converges absolutely, converges conditionally, or diverges. (summation goes to infinity and starts at k=1)

i don't think it converges absolutely, but im really not sure how to test for conditional convergence. thanks in advance

**Prove It** · October 2nd 2012, 07:12 PM

Originally Posted by chizmin10

Determine whether the series (-1)^k-11/k+K^1/2 converges absolutely, converges conditionally, or diverges. (summation goes to infinity and starts at k=1)

i don't think it converges absolutely, but im really not sure how to test for conditional convergence. thanks in advance

At the moment this is unreadable. Please use brackets where they're needed, or better yet, learn some LaTeX.

Is this your summand? $\displaystyle \begin{align*} \frac{(-1)^{k-1}}{k + k^{\frac{1}{2}}} \end{align*}$

**chizmin10** · October 2nd 2012, 07:27 PM

no thats not it. its ((-1)^k-1)(1/(k+sqrtk))

**Plato** · October 3rd 2012, 03:25 AM

Originally Posted by chizmin10

no thats not it. its ((-1)^k-1)(1/(k+sqrtk))

Do you understand that $\sqrt{k}=k^{\frac{1}{2}}~?$

**johnsomeone** · October 3rd 2012, 04:52 AM

What does the alternating series test tell you?

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