1. ## [SOLVED]Infinite Series Problem

show that if the seriesΣuk and Σvk both diverge, then seiresΣ(uk + vk) and Σ(uk - vk) may either converge or diverge

Thank you !

2. ## that is completely ambiguous

I am sorry but if youd like me to answer you must specify do you mean $\displaystyle \sum_{u,k=0}^{\infty}v\cdot{k}$ and $\displaystyle \sum_{u,k=0}^{\infty}u\cdot{k}$ or do you mean $\displaystyle \sum_{k=0}^{\infty}u(k)$ and $\displaystyle \sum_{k=0}^{\infty}v(k)$? or what?

3. and

this one
thank you

4. Originally Posted by soleilion
show that if the seriesΣuk and Σvk both diverge, then seiresΣ(uk + vk) and Σ(uk - vk) may either converge or diverge
Consider: $\displaystyle u_k = \frac{1}{k}\,\& \,v_k = \frac{{ - 1}}{k}$

5. Originally Posted by Plato
Consider: $\displaystyle u_k = \frac{1}{k}\,\& \,v_k = \frac{{ - 1}}{k}$

your examples are both diverges by p-series

then, if they plus, Σ(uk + vk)=0 converges

if they minus Σ(uk + vk)=2/k, still diverges

is my proof right???

$\displaystyle v(k)=\frac{1}{\sqrt{k}}$ and $\displaystyle u(k)=\frac{-1}{\sqrt{k}}$ since both are divergent P-series but their addition is 0 which is convergent...