Assume that (12x)/(1x+x2) + (2x4x3)/(1x2+x4) + (4x38x7)/(1 x4+x8) + = (1 + 2x)/(1+x+x2), for

Question:

Assume that (1−2x)/(1−x+x2) + (2x−4x3)/(1−x2+x4) + (4x3−8x7)/(1 − x4+x8) +· · · = (1 + 2x)/(1+x+x2), for x < 1, and let x = 0.25. Write and execute an algorithm that determines the number of terms needed on the left side of the equation so that the left side differs from the right side by less than 10−6.