The input-output relationship of a causal stable LTI system is given as
y[n] = αy[n - 1] + βx[n]. If the impulse response h[n] of this system satisfies the condition
$$\sum\limits_{n = 0}^\infty {h\left[ n \right] = 2,} $$   the relationship between α and β is

A. $$\alpha = 1 - {\beta \over 2}$$

B. $$\alpha = 1 + {\beta \over 2}$$

C. α = 2β

D. α = -2β

Answer: Option A