Question

Să se calculeze suma : subpunctul e)
Clasa a 10-a , combinari

Answer 1

$(1+x)^n = C_{n}^0+C_{n}^1 x+C_{n}^2x^2+C_{n}^3x^3+...+C_{n}^nx^n \\ \\ (1+2)^n = C_{n}^0+C_{n}^1 2+C_{n}^22^2+C_{n}^32^3+...+C_{n}^n2^n \\ \\ \Rightarrow \boxed{C_{n}^0+2C_{n}^1+2^2C_{n}^2+2^3C_{n}^3+...+2^nC_{n}^n= 3^n}$