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whatlifeforme
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Homework Statement
Absolute, Conditional, - convergence, or Divergence.
Homework Equations
[itex]\displaystyle \sum^{∞}_{n=1} (-1)^n e^{-n} [/itex]
The Attempt at a Solution
1. Alternating Series Test
2. Ratio Test for ABsolute Convergence
1. [itex]\displaystyle (-1)^n (1/e)^n [/itex]
an > 0 for n=1,2,3,4 - YES
decreasing - YES
limit (n->inf) = 0 - YES
Converges.
2.[itex]\displaystyle (1/e)^{n+1} * (e^n) = 1/e[/itex]
limit (n->inf) = 1/e
1/e < 1
Thus, Absolute Convergence.