Find the sum of the following series to infinity :

10 – 9 + 8.1 – 7.29 + …. ∞

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 = 10 and r =


sum =


1