Does the following infinite geometric series diverge or converge? Explain. (MULTIPLE CHOICE CHOOSE ONE)

Question

7 + 21 + 63 + 189 + . . .

 

a. It converges; it does not have a sum.
b. It diverges; it does not have a sum.
c. It diverges; it has a sum.
d. It converges; it has a sum.

Answer 1

Thomas has it;  the numbers are too large and just getting larger (infinitely large).  Geometric series will only have a calculable sum IF the ratio  is LESS THAN 1; the #s will be getting SMALLER (closer to zero...)

Answer 2

The following series equal to   ∑7*3ⁱ => 7(∑3ⁱ)

It doesn't have any sum and it's diverges.

So the answer is number B.

Answer 3

The answer is b.  The sum of a geometric series is give by a/(1-r) where a is the first term and r is the ratio between the terms. r=3 in the series  you have given.  The absolute value of r must be less than 1 for a geometric series to converge.