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 =


2r=2 or r= 1/2

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

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