Given the power series expansion
[infinity]
tan⁻¹ (x) = Σ (-1)ⁿ x²ⁿ⁺¹/2n+1
n=1

Determine how many terms N of the sum evaluated at x = 1 are needed to approximate tan⁻¹ (1) = π/4 accurate to within 1/1000.
N = __