Does the following infinite series converage or diverge? explain you're answer.[tex] \frac{3}{2} + \frac{12}{2} + \frac{48}{2} + \frac{192}{2} + /tex]a. it converges; it has a sumb. it diverges; it has a sumc. it diverges; it does not have a sumd. it converges; it does not have a sum

Just a quick addition to the posting above.

the sum of a geometric serie will converge when the "common ratio" is a "proper" fraction, namely a value between 0 and 1, notation wise 0 < | r | < 1.

so, we can always get the "common ratio" by simply dividing any subsequent term by the one before it, their quotient is the common ratio "r".

now if we do that here, pick any  hmmm say (192/2) ÷ (48/2), we get 4, and likewise with the other pairs, so, our "common ratio" is 4.

now  r = 4, and 4 is not a fraction, so the sum of the geometric sequence doesn't reach a fixed value,  namely it does not coverge, so it's divergent, since it goes to ∞.