1. ## Absolute convergence

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

2. ## Re: Absolute convergence

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 \displaystyle \begin{align*} \frac{(-1)^{k-1}}{k + k^{\frac{1}{2}}} \end{align*}

3. ## Re: Absolute convergence

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

4. ## Re: Absolute convergence

Originally Posted by chizmin10
no thats not it. its ((-1)^k-1)(1/(k+sqrtk))
Do you understand that $\displaystyle \sqrt{k}=k^{\frac{1}{2}}~?$

5. ## Re: Absolute convergence

What does the alternating series test tell you?