If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

If three positive numbers a, b and c are in A.P. such that abc = 8, then the minimum possible value of b is :

Let

S_n = $${1 \over {{1^3}}}$$$$ + {{1 + 2} \over {{1^3} + {2^3}}} + {{1 + 2 + 3} \over {{1^3} + {2^3} + {3^3}}} + ......... + {{1 + 2 + ....... + n} \over {{1^3} + {2^3} + ...... + {n^3}}}.$$

If 100 S_n = n, then n is equal to :

If the sum of the first n terms of the series $$\,\sqrt 3 + \sqrt {75} + \sqrt {243} + \sqrt {507} + ......$$ is $$435\sqrt 3 ,$$ then n equals :