Answer :

Let,


x = 0.231231231231…..


x = 0.231 + 0.000231 + 0.000000231 + …∞


x = 231(0.001 + 0.00001 + 0.0000001 + …∞ )


x =


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


Common ratio = 1/1000 and first term (a) = 1/1000


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


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


we can use the formula for the sum of infinite GP.


x = 231×


x = 231/999


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