Let
T=n=1∑∞(−1)n−12n−11
be an alternating series involving the reciprocals of odd integers.
(a) Compute the fifth partial sum S5=n=1∑5(−1)n−12n−11. Present your answer as a single simplified fraction.
(b) Determine the smallest positive integer N such that the absolute error ∣T−SN∣ is less than 0.005. Show all work leading to your value of N. (Do not attempt to evaluate the infinite series itself.)