Answer:
n = 7
Step-by-step explanation:
Recalling Taylor nth polynimial, we have,
Pₙ (x) = f (a) f
¹ (a) (x −a) + f
¹¹ (a) (x −a)²/2 + f
¹¹¹ (a) (x −a)³/3x2 + .......+ f ⁽ⁿ⁾ (a) (x-a)ⁿ / n (n - 1) (n - 2) .......3x2
Therefore,
If f(x) = ( 1 - x) ⁻¹ ,
Then the Lagrange form of the remainder hold which sates that,
( 1 - x) ⁻¹ - Pₙ (x) = f ⁿ⁺¹ (c) x ⁿ⁺¹ / (n + 1) !
Noting that,
where C is between 0 and x,
Hence therefore, the error is bounded by,
/ (0.5) ⁿ⁺¹ ( 1 - x) ⁻¹ ⁽⁰⁵⁾ ÷ (n + 1) !/ ≤ 10⁻⁶
These then equates to the fact that, that inequality first equates to 7.
Therefore, n = 7.
