Use principle of mathematical induction to prove that:`1+2+3+……….+n=(n(n+1))/2`

By Mathematical Induction, prove that : n! 1 .

Using principle of mathematical induction, prove that: 1+3+5+………..+(2n-1)= n^2 .

Use the principle of mathematical induction to prove that for all n in N sqrt(2+sqrt(2+sqrt(2+...+...+sqrt2)))=2cos ((pi)/(2^(n+1))) when the LHS contains n radical signs.

Use the Principle of Mathematical Induction to prove that n(n + 1) (2n + 1) is divisible by 6 for all n in N.

Apply the principle of Mathematical Induction to prove that : |sin nx| le n|sin x| for all n in N.

By Principle of Mathematical Induction, prove that : 2^n >n for all n in N.

Use the principle of mathematical induction to show that 5^(2n+1)+3^(n+2).2^(n-1) divisible by 19 for all natural numbers n.

Prove the following by using the principle of mathematical induction for all n in N :- 1 +2 + 3 +...+n < 1/8(2n+1)^2 .

Prove the following by using the principle of mathematical induction for all n in N :- n(n +1) (n + 5) is a multiple of 3.