I have basic weighted function

a = a*(1- alpha) + b*alpha

a = a + alpha*( b - a )

where

0 < alpha < 1

I should figure out how many ( n ) times I have to iterate before

abs( a_n - b) is almost zero.

I have calculated formulas for four iterations if it helps to solve the problem:

a1 = a + alpha*(b-a)

a2 = a + 2*alpha*(b-a) - 1*alpha^2*(b-a)

a3 = a + 3*alpha*(b-a) - 3*alpha^2*(b-a) + alpha^3*(b-a)

a4 = a + 4*alpha*(b-a) - 6*alpha^2*(b-a) + 4*alpha^3*(b-a) - alpha^4*(b-a)

thank you,

Markus