Let `A_n = (3/4) -(3/4)^2 + (3/4)^3 +.....+(-1)^(n - 1) (3/4)^n` , B_n = 1 - A_n . Find a least odd natural number `n_0`, so that `B_n gt A_n forall n ge n_0`.

If n is natural number & n ge 1, then (3^(2n) - 1) is always divisible by

If X = { 4^n-3n-1: n in N} and Y = { 9(n-1):n in N } where N is the set of natural numbers then X cup Y is equal to

If n is a natural number, then (4^(n) -3n -1) is always divisible by-

If .^(n-1)c_3+^(n-1)c_4gt^nc_3 then n is greater than

Let a_n=(1000)^n/(n!) for n in N . Then a_n is greatest, when

If a_n=sin^n theta+cosec^ntheta and a_1=2 prove that, a_n=2 .

Compute the division : (a^(3^n)-b^(3^n))/(a^(3^(n-1))-b^(3^(n-1))) .

lim_(n->oo)(-3n+(-1)^n)/(4n-(-1)^n) is equal to a. -3/4 b. 0 if n is even c. -3/4 if n is odd d. none of these

Let lta_ngt be the sequence defined by a_1=3 and a_n =3a_(n-1)+2 for all n gt1 ..Find a_3 .

If f and g are two functions defined on N , such that f(n)= {{:(2n-1if n is even), (2n+2 if n is odd):} and g(n)=f(n)+f(n+1) Then range of g is (A) {m in N : m= multiple of 4 } (B) { set of even natural numbers } (C) {m in N : m=4k+3,k is a natural number (D) {m in N : m= multiple of 3 or multiple of 4 }