SOLUTION: Does the infinite geometric series diverge or converge? Explain. 2+6+18+54+... a - It diverges: it does not have a sum. b - It converges: it does not have a sum c - It dive

Algebra ->  Sequences-and-series -> SOLUTION: Does the infinite geometric series diverge or converge? Explain. 2+6+18+54+... a - It diverges: it does not have a sum. b - It converges: it does not have a sum c - It dive      Log On

It diverges; it does not have a sum.

Reason: a geometric series converges if and only if
the common ratio, r, is such that |r| < 1, and
diverges if |r|>=1.  The common ratio here is r = 3.

Edwin