Question

Does the infinite geometric series diverge or converge? Explain.

Answer 1

it converges, since the common ratio (1/2) is less than unity,1. That is the rule. if the common ratio of an infinite geometric series is less than unity, it converges, or otherwise it diverges.

Answer 2

ohh okay does it have a sum? or it does not have one

Answer 3

yes, it has the sum, \[\frac{ a }{ 1-r }\]\[\frac{ 1/5 }{ 1-1/2 }\]\[\frac{ 2 }{ 5 }\]
'a ' represents the first term and 'r' represents the common ratio.

Answer 4

ohh okay thank you!