Prove that following identities:
C(n,n) = 1

Prove the following identity : 2u_6-3u_4+1=0 , where u_n =cos^n theta+ sin^n theta .

Prove the following by using induction for all n in N . 1+2+3+.....+n=(n(n+1))/(2)

Prove the following: sin (n + 1)x sin (n + 2)x + cos (n + 1)x cos (n + 2)x = cos x

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.

Prove the following by using the principle of mathematical induction for all n in N :- 10^(2n-1) + 1 is divisible by 11.

Prove the following by using the principle of mathematical induction for all n in N :- 1.2.3 + 2.3.4 +...+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4 .

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 :- 1 +3 + 3^2 +....+3^(n-1)=((3^n-1))/2 .

Prove the following by using the principle of mathematical induction for all n in N :- a + ar + ar^2+...+ ar^(n-1)=(a(r^n-1))/(r-1) .