Question

...................................

Answer 1

Explicație pas cu pas:

x=1 => p(x)=

$\frac{1}{1 \times 4} = \frac{1}{3 \times 1 + 1}$

=> p(x) adev

presupun p(x) adev -> p(x+1) adev

$\frac{1}{4} + ... + \frac{1}{(3x - 2)(3x + 1)} + \frac{1}{(3x + 1)(3x + 4)} = \frac{x + 1}{3x + 4} \\ \frac{x}{3x + 1} + \frac{1}{(3x + 1)(3x + 4)} = \frac{x + 1}{3x + 4} \\ x(3x + 4) + 1 = (x + 1)(3x + 1) \\ 3 {x}^{2} + 4x + 1 = 3 {x}^{2} + 4x + 1$