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lilypetals
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Homework Statement
[tex]\Sigma[/tex] from n=0 to infinity (-10)n/n!
Determine the absolute convergence, convergence, or divergence of the series.
Homework Equations
In this section, it's suggested that we use the following to determine a solution:
A series is called absolutely convergent if the series of absolute values [tex]\Sigma[/tex]|an| is convergent.
The Comparison Test, which states that if the series bn is convergent and greater than the series an, then the series an is also convergent; and if the series bn is divergent and less than the series an, then the series an is also divergent.
The Ratio Test, which states that if the limit as n goes to infinity of |an+1/an| is less than 1 the series is absolutely convergent; if it is greater than 1 the series is divergent; and if it is equal to 1 the Ratio Test is inconclusive.
The Root Test, which states that if the limit as n goes to infinity of the nth root of an is less than 1 the series is absolutely convergent; if it is greater than 1 the series is divergent; and if it is equal to 1 the Root Test is inconclusive.
The Attempt at a Solution
I decided that the simplest method would be to apply the Comparison Test to the series of absolute values:
[tex]\Sigma[/tex] n=0 to infinity |(-10)n|/n!
So, I need to consider a bn which is greater than an, which converges.
This is where I get stuck. I haven't been able to find a bn for which I could solve the limit as n goes to infinity. Anyone have a good method for this?