Answer :

We observe that above progression possess a common ratio, but alternatively , adjacent terms are not possessing a common ratio. So, it consists of 2 geometric progressions.


Let, S =


S =


Let us denote the two progressions with S1 and S2


S = S1 + S2


S1 =


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 = 1/9


S1 =


S2 =


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 = 1/25


S2 =


Hence,


S =


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