Find all values of x in which the series converges

[turbokaz]

Homework Statement

Find all values of x for which the series Ʃ (4x+5)^n/2^n converges. (n=0; n→∞)
Answer choices: (3/4,-3/4)
(3/4,7/4)
(-7/4,7/4)
(-5/4,5/4)
(-7/4,-3/4)

Homework Equations

The Attempt at a Solution

I think the answer is -7/4,-3/4. If I remember correctly, there is a test that states that a series converges if the limit goes to 0. Is this correct?

 

[tiny-tim]

hi turbokaz!

(yes, correct answer)

look at it this way …

it's ∑ aⁿ where a = (4x+5)/2

so what is the equation for when ∑ aⁿ converges?