If the arithmetic mean of the product of all pairs of positive integers whose sum is n is `A_n` then `lim_(n->oo) n^2/(A_n)` equals to

If the arithmetic mean of the product of all pairs of positive integers whose sum is n is A_(n) then lim_(n rarr oo)(n^(2))/(A_(n)) equals to

lim_(nto oo) (2^n+5^n)^(1//n) is equal to

If the sum of the first n terms of an arithmetic progression, whose first term is the sum of the first n positive integers and whose common difference is n, is (8n^(2)-11n-20) , then the sum of all the possible values of n is

lim_(n rarr oo)(n!)/((n+1)!+n!) is equal to

lim_(n rarr oo)(n!)/((n+1)!+n!) is equal to

lim_(n to oo) (3^(n)+4^(n))^(1//n) is equal to

8. Let S, be a square of unit area. A circle C_1, is inscribed in S_1, a square S_2, is inscribed in C_1 and so on. In general, a circle C_n is inscribed in the square S_n, and then a square S_(n+1 is inscribed in the circle C_n. Let a_n denote the sum of the areas of the circle C_1,C_2,C_3,.....,C_n then lim_(n->oo) a_n must be

Let a_1,a_2,a_3…………., a_n be positive numbers in G.P. For each n let A_n, G_n, H_n be respectively the arithmetic mean geometric mean and harmonic mean of a_1,a_2,……..,a_n On the basis of above information answer the following question: A_k,G_k,H_k are in (A) A.P. (B) G.P. (C) H.P. (D) none of these