" For every tre integer "sqrt(n-1)+sqrt(n+1)" is : "

Show that there is no positive integer, n for which sqrt(n-1) + sqrt(n+1) is rational .

Show that there is no positive integer n for which sqrt(n-1)+sqrt(n+1) is rational.

Show that there is no positive integer n for which sqrt(n-1)+sqrt(n+1) is rational.

Statement -1 : For every natural number n ge 2, (1)/( sqrt1) + (1)/( sqrt2) + (1)/( sqrt3) + … + (1)/( sqrtn) gt sqrtn . Statement - 2 : For every natural number n ge 2, sqrt(n(n+1) ) lt n+1

The least positive integer n for which sqrt(n+1) - sqrt(n-1) lt 0.2 is

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

For every integer n ge 1, (3^(2n) -1) is divisible by

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

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