Infinite Sequences Series

Infinite Series Error Bounds

Estimate the error when approximating infinite series with partial sums using error bound theorems. For alternating series, the error is bounded by the absolute value of the first omitted term. For Taylor series, use the Lagrange error bound |Rₙ(x)| ≤ M|x-a|^(n+1)/(n+1)! where M is the maximum of |f^(n+1)| on the interval. Practice determining how many terms are needed to achieve a desired accuracy.