Alternating Series Remainder Theorem Worksheet
Practice problems on the Alternating Series Remainder Theorem for Grade 9 Calculus students.
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Alternating Series Remainder Theorem
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Read each question carefully and show all your work. Use the Alternating Series Remainder Theorem to estimate the error bounds.
1. The Alternating Series Remainder Theorem states that if an alternating series satisfies the conditions of the Alternating Series Test, then the absolute value of the remainder R_n is less than or equal to the absolute value of the term.
2. For the series Σ (-1)^(n+1) * (1/n), if we approximate the sum using the first 4 terms, the maximum error is given by the term.
1. Consider the alternating series Σ (from n=1 to infinity) of (-1)^(n+1) / n!. If you approximate the sum of this series using the first 5 terms, what is the maximum possible error in your approximation?
1. For the alternating series Σ (from n=1 to infinity) of (-1)^n / (n^2 + 1), which of the following is the smallest number of terms needed to guarantee that the approximation of the sum is within 0.01 of the actual sum?
9 terms
10 terms
11 terms
12 terms
1. The alternating series Σ (from n=0 to infinity) of (-1)^n / (2n+1) converges to π/4. If you use the first 3 terms of this series to approximate π/4, what is the maximum error in your approximation? Show your work.