Find the sum of the following series to infinity :

2/5 + 3/5² + 2/5³ + 3/5⁴ + …. ∞

We observe that the above progression possess a common ratio. So it is a geometric progression.

Common ratio = r =

Sum of infinite GP = ,where a is the first term and r is the common ratio.

Note: We can only use the above formula if |r|<1

Clearly, a = and r =

⇒ sum =