show that if the seriesΣuk and Σvk both diverge, then seiresΣ(uk + vk) and Σ(uk - vk) may either converge or diverge
Thank you !
Last edited by soleilion; April 5th 2008 at 03:43 PM.
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I am sorry but if youd like me to answer you must specify do you mean and or do you mean and ? or what?
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:
Originally Posted by Plato Consider:
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???
and since both are divergent P-series but their addition is 0 which is convergent...
Take the general example of 1/x^a and -1/x^a with a =< 1 (Riemann series)
You can also take a look at alternated series
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