If C₀, C₁, C₂, ......, C_n denote the coefficients in the expansion of (1 + x)ⁿ then the value of C₁ + 2C₂ + 3C₃ + ..... + nC_n is

If the coefficients of x² and x³ in the expansion of (3 + ax)⁹ be same, then the value of a is

using binomial theorem, the value of (0.999)³ correct to 3 decimal places is

$$({2^{3n}} - 1)$$ will be divisible by $$(\forall n \in N)$$