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By using The Ratio Test determine if the series is convergent: `sum` `a^n/2^n`
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Using the Ratio Test gives the convergence of the series if
`lim(n->oo) |a_(n+1)/a_n| < 1`
= `lim(n->oo) a^(n+1 - n)/2^(n+1 - n)`
= `lim(n->oo) a/2`
`a/2` is less than, equal to or greater than 1 depending on what the value of a is. Here, the value of a is not given.
It is not possible to determine if the given series is convergent using the Ratio Test.
Posted by justaguide on April 29, 2013 at 5:43 AM (Answer #1)
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