Given the following:
. . .\(\displaystyle x\, -\, \dfrac{y}{2}\, +\, \dfrac{x}{3}\, -\, \dfrac{y}{4}\, +\, \dfrac{x}{5}\, -\, \dfrac{y}{6}\, +\, ...\)
...with \(\displaystyle x,\, y\, >\, 0,\) for what values of \(\displaystyle x\) and \(\displaystyle y\) does this series converge conditionally, and for what values does it converge absolutely?
I think I need to consider when x>y, x<y, and x=y. And I know that I need to use the alternating series test.
But I am still lost..
Any help will be appreciated!!
. . .\(\displaystyle x\, -\, \dfrac{y}{2}\, +\, \dfrac{x}{3}\, -\, \dfrac{y}{4}\, +\, \dfrac{x}{5}\, -\, \dfrac{y}{6}\, +\, ...\)
...with \(\displaystyle x,\, y\, >\, 0,\) for what values of \(\displaystyle x\) and \(\displaystyle y\) does this series converge conditionally, and for what values does it converge absolutely?
I think I need to consider when x>y, x<y, and x=y. And I know that I need to use the alternating series test.
But I am still lost..
Any help will be appreciated!!
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