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 =


1