Consider the Series: ∑ 1/[2^(k+(-1)^k)] from k=0 to ∞. a. Use the ratio test to show the limit does not exist. b. Use the root test to show the series converges.
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Originally Posted by jules027 Consider the Series: ∑ 1/[2^(k+(-1)^k)] from k=0 to ∞. a. Use the ratio test to show the limit does not exist. b. Use the root test to show the series converges. Setting up the ratio test we get Which is an oscilating function...to realize this also notice that In this case only because Next if we do the root test we get Thus since this is less than one the series converges
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