Approximating Sums of Alternating Series

Theorem. If an alternating collection satisfies the speculation of the alternating collection take a look at, and if S could be the sum of your sequence, then either sn≤S≤sn+1 or sn+1≤S≤sn, and if S is approximated by sn, then the absolute error |S−sn| satisfies|S−sn|≤an+1.Furthermore, the sign of the error S−sn is the same as an+one.Evidence. From the evidence in the Alternating Sequence Take Read more…