Does the following infinite series converge or diverge? 1/3+2/9+4/27+8/81+
a. it diverges, it has a sum
b. it's converges, it has a sum
c. it diverges, doesn't have a sum
d. it converges, doesn't have a sum

Note that A and D are ludicrous choices, so you can throw them away outright. (Any divergent series cannot have a sum, and any convergent series must have a sum.)

The sum is certainly convergent because it can be written as a geometric sum with common ratio between terms that is less than 1 in absolute value.




We can then find the exact value of the sum:







So the answer is B.