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  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)

Answer 1

a_n = (-1)ⁿ/(2n)!

1/0! = 1.0

-1/2! = -0.5

1/4! = 0.04166

-1/6! = -0.001388

1/8! = 0.0000248 which is less than 0.0001 error, so more terms won't contribute much

Sum = 1 - 0.5 + 0.04166 - 0.001388 + 0.0000248 ≈ 0.5403