Homework Help

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

user profile pic

Rocky52 | Student, Undergraduate | Honors

Posted April 29, 2013 at 5:04 AM via web

dislike 1 like

By using The Ratio Test determine if the series is convergent:

`sum` `a^n/2^n`

1 Answer | Add Yours

user profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 29, 2013 at 5:43 AM (Answer #1)

dislike 1 like

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.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes