Solution Found!
Estimating infinite sums Estimate the value of the
Chapter 10, Problem 36E(choose chapter or problem)
35-38. Estimating infinite sums Estimate the value of the following convergent series with an absolute error less than \(10^{-3}\).
\(\sum_{k=1}^{\infty} \frac{(-1)^{k}}{(2 k+1)^{3}}\)
Questions & Answers
QUESTION:
35-38. Estimating infinite sums Estimate the value of the following convergent series with an absolute error less than \(10^{-3}\).
\(\sum_{k=1}^{\infty} \frac{(-1)^{k}}{(2 k+1)^{3}}\)
ANSWER:Problem 36E
Estimating infinite sums Estimate the value of the following convergent series with an absolute error less than 10−3.
Answer;
Step 1;
In this problem we need to Estimate the value of the convergent series with an absolute error less than
.
Alternating series error bound ; For a decreasing , alternating series , it is easy to get a bound on the error :
||
……………(1)
In other words , the error is bounded by the next term in the series.