The number of positiveintegers n in the set (1,2, 3,. .00) for which the number `(1^2+2^2+3^2+...+n^2)/(1+2+3...n)` is an integer is

The number of positive integers n in the set {1, 2, 3, .......100} for which the number (1^(2)+2^(2)+3^(2)+......+n^(2))/(1+2+3+......+n) is an integer is

The number of positive integers n in the set {2,3,....,200} such that (1)/(n) has a terminating decimal expansion is

The sum of all positive integers n for which (1^3+2^3+....(2n)^3)/(1^2+2^2+....+n^2) is also an integer is

If the numbers of solutions in positive integers of 2x + 3y = 763 is N, then find (N-2)^(1/3)

Consider the following statements : 1. Nuu(BnnZ)=(NuuB)nnZ for any subset B of R , where N is the set of positive integers, Z is the set of integers, R is the set of real numbers. 2. Let A={n in N : 1 ge n ge 24, n "is a multiple of" 3} . There exists no subsets B of N such that the number of elements in A is equal to the number of elements in B . Which of the above statemetns is/are correct ? (A) 1 only (B) 2 only (C) Both 1 and 2 (D) Neither 1 nor 2

For a positive integer n let a(n)=1+1/2+1/3+1/4+….+1/ ((2^n)-1) Then

Mean of the numbers 1,2,3,..., n with respective weights 1^(2)+1,2^(2)+2,3^(2)+3,......,n^(2)+n is

Let f be a function from the set of positive integers to the set of real number i.e f : N rarr R , such that f(1) + 2f{2} + 3f{3} + ….. + nf{n} = n(n + 1) f(n) for n ge 2 Then the of 1/f(4) must be

For a positive integer n let a(n)=1+1/2+1/3+1/4+.......+1/((2^n)-1) then

Mean of the numbers 1,2,3,..., , n with respective weights 1^(2)+1,2^(2)+2,3^(2)+3,......,n^(2)+n is