Prove the following by using the principle of mathematical induction for all

a + (a + d) + (a + 2d) + ...........+ [a + (n - 1)d] =

Prove the following by using the principle of mathematical induction for all :

Prove the following by using the principle of mathematical induction for all

Prove the following by using the principle of mathematical induction for all .

Prove the following by using the principle of mathematical induction for all

n (n + 1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all

is a multiple of 27 for all

Prove the following by using the principle of mathematical induction for all

is divisible by 11.

Prove the following by using the principle of mathematical induction for all

is divisible by 8.

Prove by mathematical induction that sum of cubes of three consecutive natural numbers is divisible by 9.

Show by mathematical induction that a²ⁿ – b²ⁿ is divisible by a + b.