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49. Sigma notation Evaluate the following expressions. 10 Σκ k k=1 6 b. Σ (2k + 1) k=1 4 a. C. k2 k=1 5 d. Σ(1 + n?) n=1

49. Sigma notation Evaluate the following expressions. 10 Σκ k k=1 6 b. Σ (2k + 1) k=1 4 a. C. k2 k=1 5 d. Σ(1 + n?) n=1

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 5E
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(Question 49 a-d and question 56)

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T 55-58. Approximating areas with a calculator Use a calculator and right Riemann sums to approximate the area of the given region. Present your calculations in a table showing the approximations for n = 10, 30, 60, and 80 subintervals. Make a conjecture about the limit of Riemann sums as n → ∞. 55. The region bounded by the graph of f(x) = 12 - 3x² and the x-axis on the interval [-1, 1]. 56. The region bounded by the graph of f(x) = 3x² + 1 and the x-axis on the interval [—1, 1]. 57. The region bounded by the graph of f(x) = the interval [-π, π]. 1 - cos x 2 and the x-axis on
Transcribed Image Text:T 55-58. Approximating areas with a calculator Use a calculator and right Riemann sums to approximate the area of the given region. Present your calculations in a table showing the approximations for n = 10, 30, 60, and 80 subintervals. Make a conjecture about the limit of Riemann sums as n → ∞. 55. The region bounded by the graph of f(x) = 12 - 3x² and the x-axis on the interval [-1, 1]. 56. The region bounded by the graph of f(x) = 3x² + 1 and the x-axis on the interval [—1, 1]. 57. The region bounded by the graph of f(x) = the interval [-π, π]. 1 - cos x 2 and the x-axis on
49. Sigma notation Evaluate the following expressions. 10 ΣΕ k=1 6 a. b. Σ(2k + 1) k=1 4 Στα k=1 5 d. Σ(1 + n?) n=1 3 Σ m=1 3 †. Σ(3; - 4) j=1 5 9. Σ(2p + p3) p=1 C. e. 2m + 2 3
Transcribed Image Text:49. Sigma notation Evaluate the following expressions. 10 ΣΕ k=1 6 a. b. Σ(2k + 1) k=1 4 Στα k=1 5 d. Σ(1 + n?) n=1 3 Σ m=1 3 †. Σ(3; - 4) j=1 5 9. Σ(2p + p3) p=1 C. e. 2m + 2 3
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