PLEASE HELP!!! Does The Following infinite series converage or diverge? Explain You're answer. (3)/(2) + (12)/(2) + (48)/(2) + (192)/(2) + .... A. It Converges; it has a su…

Question

PLEASE HELP!!!

Does The Following infinite series converage or diverge? Explain You're answer.


`(3)/(2) + (12)/(2) + (48)/(2) + (192)/(2) + ....`
A. It Converges; it has a sum

B. It Diverges; it has a sum

C. it diverges; it does not have a sum

D. It Converges; it does not have a sum

Answer 1

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 ∞.

Answer 2

Answer:

diverges to infinity

Step-by-step explanation:

This is the same as:
32+6+24+96+...

By observation each successive term is greater than the previous so the sum is always increasing. As it is an infinite series the sum must eventually reach infinity.

So the sum is infinity →∞

Some would argue that it does not have a sum as infinity is not measurable. On the other hand I have come across the phrase 'sums to infinity'. So I am not sure if you could or could not describe this as: "diverges, has a sum"