(4CQ) Determine whether the series 3/2+9/8+27/32+...is convergent or divergent.

Answer:The series is convergent ⇒ answer (a)Step-by-step explanation:* The series is 3/2 + 9/8 + 27/32 + ........- It is a geometric series with:- first term a = 3/2 and common ratio r = 9/8 ÷ 3/2 = 3/4* The difference between the convergent and divergent   in the geometric series is :- If the geometric series is given by  sum  = a + a r + a r² + a r³ + ... * Where a is the first term and r is the common ratio* If |r| < 1 then the following geometric series converges to a / (1 - r).  - Where a/1 - r is the sum to infinity* The proof is:∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number∴ r^n approach to zero∴ S = a(1 - 0)/(1 - r) = a/(1 - r)∴ S∞ = a/1 - r* If |r| ≥ 1 then the above geometric series diverges∵ r = 3/4∴ r < 1∴ The series is convergent