Estimate the sum of the alternating series the sum from n equals 0 to infinity of the quotient of negative 1 raised to the nth power and the quantity 2 times n factorial within an error of 0.0001.

Question

Estimate the sum of the alternating series the sum from n equals 0 to infinity of the quotient of negative 1 raised to the nth power and the quantity 2 times n factorial within an error of 0.0001.
Type your answer in the space below and give six decimal places. If your answer is less than 1, place a leading "0" before the decimal point (ex: 0.482317). (10 points)

oobleck · Answer

well, cos(x) = 1 - x^2/2! + x^4/4! - ... Your series is 1 - 1/2! + 1/4! - ... so, what do you think?