(8CQ) Determine whether the series -5+25-125+... is convergent or divergent.

Answer:The answer is divergent ⇒ answer (b)Step-by-step explanation:* The series is -5 + 25 + -125 + ........- It is a geometric series with:- first term a = -5 and common ratio r = 25/-5 = -5* 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 = -5∴ IrI = 5∴ IrI > 1∴ The series is divergent