Check whether `4^n` can end with the digit 0 for any natural number n.

Check whether 6^n can end with the digit 0 for any natural number n.

Check whether 3^n can end with the digit 0 for any natural number n.

Find the sum of first n natural numbers.

The mean of the cubes of the fist n natural number is

Find the mean and variance of the first n natural numbers.

Write the negation of the following statements and check whether the resulting statements are true, Every natural number is greater than 0.

The last four digits of the natural number 3^100 are

Statement 1 The difference between the sum of the first 100 even natural numbers and the sum of the first 100 odd natural numbers is 100. Statement 2 The difference between the sum opf the first n even natural numbers and sum of the first n odd natural numbers is n.

Use the principle of mathematical induction to show that a^(n) - b^n) is divisble by a-b for all natural numbers n.