Let I(n) = nⁿ, J(n) = 13.5 ......... (2n $$ - $$ 1) for all (n > 1), n $$ \in $$ N, then

Given that n numbers of arithmetic means are inserted between two sets of numbers a, 2b and 2a, b where a, b $$ \in $$ R. Suppose further that the mth means between these sets of numbers are same, then the ratio a : b equals

In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of this GP series is

If a, x are real numbers and | a | < 1, | x | < 1, then 1 + (1 + a) x + (1 + a + a²) x² + ..... $$\infty $$ is equal to