Answer :

As we have the first term of GP. Let r be the common ratio.


we can say that GP is 1 , r , r2 , r3 … ∞


As per the condition, each term is the sum of all terms which follow it.


If a1,a2 , … represents first, second, third term etc


we can say that:


a1 = a2 + a3 + a4 + …∞


1 = r + r2 + r3 +…∞


Note: You can take any of the cases like a2 = a3 + a4 + .. all will give the same result.


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


Common ratio = r and first term (a) = r


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.


S =





r=1−r



2r=2 or r= 1/2



Hence the series is 1, 1/2, 1/4, 1/8, 1/16...............


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