Show that the square roots of two successive natural numbers greater than `N^2` differ by less than `1/(2N)dot`

The AM of the squares of the first 'n' natural numbers is

Prove that (n !+1) is not divisible by any natural number between 2 and n

Find all pairs of consecutive odd natural numbers both of which are larger than 10 and their sum is less than 40.

Write the negation of the following statements: The number 2 is greater than 7.

Standard deviation of the first 2n+1 natural numbers is equal to

Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as i. number greater than 4 ii. six appears on atleast one die

If S_1, S_2, S_3 are the sum of first n natural numbers, their squares and their cubes, respectively , show that 9 S_(2)^(2) = S_(3) (1+ 8S_1)