Question

Does the infinite geometric series diverge or converge?
1/6+1/12+1/24+1/48+...
a.It diverges;it does not have a sum
b.It diverges;it has a sum
c.It converges;it has a sum
d. It converges;it does not have a sum

Answer 1

\[\frac{ 1 }{ 6 }+\frac{ 1 }{ 12 }+\frac{ 1 }{ 24 }+\frac{ 1 }{ 48 }+....\]

Answer 2

This geometric series has ratio 1/2
DEFINITION:If r is between −1 and +1, the terms of the series become smaller and smaller, approaching zero in the limit and the series converges to a sum

Answer 3

So the correct answer is "C."