Determine whether the infinite geometric series converges or

Determine whether the infinite geometric series converges or diverges. If it converges find its sum.

Answer: The series (converges, diverges).

Solution

1/2 +5/2 +5^2/2 ---- = 1/2( 1 +5 +5^2 ......)

Its geometrice series common ratio r= 5

Since r> 1 .The sum S = a/(1-r) of series diverges.

Answer : diverges