The sequence of positive numbers u₁, u₂, u₃, … is such that u₁ > 4 and, for n ≥ 1, uₙ₊₁ = (uₙ²+uₙ+12)/(2uₙ).

It is given that y = (1 + x)² ln(1 + x). Find d³y/dx³. Prove by mathematical induction that, for every integer n ≥ 3,…

It is given that u_r = r × r! for r = 1, 2, 3, ... . Let S_n = u_1 + u_2 + u_3 + ... + u_n. Write down the values of …

Given that a is a constant, prove by mathematical induction that, for every positive integer n, dⁿ/dxⁿ(xeᵃˣ) = naⁿ⁻¹e…

Use de Moivre's theorem to show that sin 5θ = 5 sin θ – 20 sin³ θ + 16 sin⁵ θ.

The roots of the cubic equation x³- 5x² + 13x – 4 = 0 are α, β, γ.

It is given that A= 2 3 1 0 -2 1 0 0 1