Identify the alternating series in the form (sum (-1)^{n}a_n) or (sum (-1)^{n+1}a_n), where (a_n ge 0)
Check that (a_n) decreases monotonically
Check that (lim_{ntoinfty} a_n = 0)
Use the Alternating Series Estimation Theorem
For the partial sum (S_N), the error satisfies (|R_N| = |S – S_N| le a_{N+1})
Use the next omitted term (a_{N+1}) as the error bound
For a desired accuracy (epsilon), choose (N) so that (a_{N+1} le epsilon)
If needed, use the sign of the next omitted term to determine whether (S_N) is an overestimate or underestimate
For alternating series with decreasing terms, the true sum lies between consecutive partial sums
Use (|S – S_N| le text{first omitted term}) as the standard error estimate