Statement-1: For every natural number `n ge 2, (1)/(sqrt1)+(1)/(sqrt2)+…..(1)/(sqrtn) gt sqrtn`
Statement-2: For every natural number `n ge 2, sqrt(n(n+1) lt n+1`

Statement-1: For every natural number nge2 , (1)/(sqrt(1))+(1)/(sqrt(2))+(1)/(sqrt(3))+...+(1)/(sqrt(n))gtsqrt(n) Statement-2: For every natural number nge2, sqrt(n(n+1))ltn+1

Prove that 1+(1)/(sqrt2)+(1)/(sqrt3)+....+(1)/(sqrtn) ge sqrtn, AA n in N

If n is a natural number, then sqrt(n) is:

Statement -1 For each natural number n,(n+1)^(7)-n^7-1 is divisible by 7. Statement -2 For each natural number n,n^7-n is divisible by 7.

For all n in N, 1 + 1/(sqrt(2))+1/(sqrt(3))+1/(sqrt(4))++1/(sqrt(n))

Statement - I : The variance of first n even natural numbers is (n^(2) - 1)/(4) Statement - II : The sum of first n natural numbers is (n(n+1))/(2) and the sum of the squares of first n natural numbers is (n(n+1)(2n+1))/(6)

Statement-1 For all natural number n, 1+2+....+nlt (2n+1)^2 Statement -2 For all natural numbers , (2n+3)^2-7(n+1)lt (2n+3)^3 .

Show that n^3+(n+1)^3+(n+2)^3 is divisible by 9 for every natural number n .

underset(nrarroo)lim[(1)/(sqrtn)+(1)/(sqrt(2n))+(1)/(sqrt(3n))+...+(1)/(n)]

Statement-1 :Variance of first n natural number is (n^2-1)/12 . Statement-2 : S.D. of first n natural number is sqrt((n^2-1)/12)