Given that `u_(n+1)=3u_n-2u_(n-1),` and `u_0=2 ,u_(1)=3`, then prove that `u_n=2^(n)+1` for all positive integer of `n`

If u_(n)=sin^(n)alpha+cos^(n)alpha , then prove that 2u_(6)-3u_(4)+1=0 .

Prove by using the principle of mathemtical induction: If u_0=2, u_1 = 3 and u_(n+1)=3u_n -2u_(n-1), show that u_n = 2^n +1, n epsilon N

If U_(n)=(sqrt(3)+1)^(2n)+(sqrt(3)-1)^(2n), then prove that U_(n+1)=8U_(n)-4U_(n-1)

If u_(n)=2Cos^(n) theta then show that u_(1)u_(n)-u_(n-1)= u_(n+1)

Consider the sequence u_n=sum_(r=1)^n r/2^r , n >= 1 then the limit_(n->oo) u_n

If n is a positive integer and U_(n) = (3 + sqrt5)^(n) + (3 - sqrt5)^(n) , then prove that U_(n + 1) = 6U_(n) - 4U_(n -1), n ge 2

If U_n=(sqrt(3)+1)^(2n)+(sqrt(3)-1)^(2n) , then prove that U_(n+1)=8U_n-4U_(n-1)dot

If U_n=(sqrt(3)+1)^(2n)+(sqrt(3)-1)^(2n) , then prove that U_(n+1)=8U_n-4U_(n-1)dot

If U_n=(sqrt(3)+1)^(2n)+(sqrt(3)-1)^(2n) , then prove that U_(n+1)=8U_n-4U_(n-1)dot

If u_n = 2cos n theta then u_1u_n - u_(n-1) is equal to