By using The Ratio Test determine if the series is convergent: `sum` `a^n/2^n`

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justaguide eNotes educator| Certified Educator

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)/2^(n+1))/(a^n/2^n)`

= `lim(n->oo) a^(n+1 - n)/2^(n+1 - n)`

= `lim(n->oo) a/2`

= `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.