1) showing points (n, an) and (n, Sn) for n = 1, 2, ..., 10, along with a horizontal line at a height equal to the sum S of the series.
2) Do the distances between the successive points and the horizontal line increase or decrease. How do the answers to these questions relate to the bound on |S - Sn| given in Theorem 9.15 in Section 9.5 (Altarnating series)?
please make sure to answer part 2 by using Alternating series
Homework Answers
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1) showing points (n, an) and (n, Sn) for n = 1, 2, ..., 10, along with a horizontal line at a he...
a,b,c and d (-1) 4. (3 points each) Consider the series n° +2n +3 (a) Prove...
a,b,c and d
(-1) 4. (3 points each) Consider the series n° +2n +3 (a) Prove that this series converges absolutely. (b) Show that this series satisfies all three conditions of the Alternating Series Test. HI11-2212, JL ILG-2020 Test #3 (c) What value of n guarantees that the partial sum 8, approximates the sum of this series to within an accuracy of 0.01? (d) Find the sum of the series with this accuracy (by finding the appropriate partial sum sn,...
10. 1.92 points RogacalcE13 10 7.047 y Notes Ask Your leacher Consider the following function. (a...
10. 1.92 points RogacalcE13 10 7.047 y Notes Ask Your leacher Consider the following function. (a) Use the Maclaurin expansion for et to express the function Fox) as an alternating power series in x. F(x) (b) Find an N such that the partial sum s of the Maclaurin series approximates the integral for x1.1 to within an error of at most 0.001 (c) Compute sw using the N found above. (Round your answer to six decimal places.) SN 7. 01.92...
3. (12 points) Consider the following sum: n Sn = {(i + 1)(i +2) i=0 (a)...
3. (12 points) Consider the following sum: n Sn = {(i + 1)(i +2) i=0 (a) Use properties of summations to find a closed form expression for Sn. Simplify your answer into a polynomial with rational coefficients. Show your work, and clearly indicate your final answer. (b) Use weak induction to prove that your closed form works for every integer n > 0. Make sure you include all three parts, and label them appropriately!
o Consider the series an whose partial sums are denoted as Sn for n > 1....
o Consider the series an whose partial sums are denoted as Sn for n > 1. n= 1 (1) If an = m+2, does an converge or diverge? Explain. n = 1 (2) If Sn = 7+2, does [ an converge or diverge? Explain. 111
1. (10 points) Consider the sum S=5+17+29+ ... +605. (a) Write the sum S in summation...
1. (10 points) Consider the sum S=5+17+29+ ... +605. (a) Write the sum S in summation notation. (b) Evaluate the sum (what is the value of S?) 2. (10 points) Consider the series (4.5* + 6). ko (a) When n = 3, write the series without summation notation, and find the sum. The series (when n = 3): The sum of the series (when n = 3): (b) Find the sum of the series for general n.
Consider the series (n=1 and infinite) ∑(−1)^(n+1) (x−3)^n / [(5^n)(n^p)], where p is a constant and...
Consider the series (n=1 and infinite) ∑(−1)^(n+1) (x−3)^n / [(5^n)(n^p)], where p is a constant and p > 0. a) For p=3 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning. b) For p=1 and x=8, does the series converge absolutely, converge conditionally, or diverge? Explain your reasoning. c) When x=−2, for what values of p does the series converge? Explain your reasoning. (d) When p=1 and x=3.1, the series converges to a value SS....
(10 points) This problem is related to Problem 9.15 in the text. Consider the periodic function...
(10 points) This problem is related to Problem 9.15 in the text.
Consider the periodic function with period 16 given by
(10 points) This problem is related to Problem 9.15 in the text Consider the periodic function with period 16 given by if 8 t<-2 if 2 t4 if 4 t<7 if 7 t8 0 -6 f(t) = 6 0 Find the first 3 coefficients of the exponential Fourier Series for f(t), i.e., F(n) for n = -2, -1,0, 1,...
11. (10 points) - MATLAB ce of the alternating harmonic series, shown below: 1-2?--+ - 3...
11. (10 points) - MATLAB ce of the alternating harmonic series, shown below: 1-2?--+ - 3 4 5 Use a loop to determine when the series has converged within a tolerance of 0.001. The animation should show how the value of the series changes as each successive term is added, resulting in a final
i 10 (1 point) Consider the series -. Let s, be the n-th partial sum; that...
i 10 (1 point) Consider the series -. Let s, be the n-th partial sum; that is, in +9 10 Sn = i +9 Find 84 and so S4 S8 =
1. Consider the difference equation (1) Sn+2 - -8n+1Sn with initial conditions so = 0, 81...
1. Consider the difference equation (1) Sn+2 - -8n+1Sn with initial conditions so = 0, 81 = 1 Let (x) n-0 denote the generating function of (sn) (a) Derive the fact that I++ = (x)f to show that (b) Use the generating function (x) r2+a+1 0 if n is a multiple of 3 1 if n is of the form 3j + 1 . -1 if n is of the form 3j 2 There are a number of ways to...
a,b,c and d
(-1) 4. (3 points each) Consider the series n° +2n +3 (a) Prove that this series converges absolutely. (b) Show that this series satisfies all three conditions of the Alternating Series Test. HI11-2212, JL ILG-2020 Test #3 (c) What value of n guarantees that the partial sum 8, approximates the sum of this series to within an accuracy of 0.01? (d) Find the sum of the series with this accuracy (by finding the appropriate partial sum sn,...
10. 1.92 points RogacalcE13 10 7.047 y Notes Ask Your leacher Consider the following function. (a) Use the Maclaurin expansion for et to express the function Fox) as an alternating power series in x. F(x) (b) Find an N such that the partial sum s of the Maclaurin series approximates the integral for x1.1 to within an error of at most 0.001 (c) Compute sw using the N found above. (Round your answer to six decimal places.) SN 7. 01.92...
3. (12 points) Consider the following sum: n Sn = {(i + 1)(i +2) i=0 (a) Use properties of summations to find a closed form expression for Sn. Simplify your answer into a polynomial with rational coefficients. Show your work, and clearly indicate your final answer. (b) Use weak induction to prove that your closed form works for every integer n > 0. Make sure you include all three parts, and label them appropriately!
o Consider the series an whose partial sums are denoted as Sn for n > 1. n= 1 (1) If an = m+2, does an converge or diverge? Explain. n = 1 (2) If Sn = 7+2, does [ an converge or diverge? Explain. 111
1. (10 points) Consider the sum S=5+17+29+ ... +605. (a) Write the sum S in summation notation. (b) Evaluate the sum (what is the value of S?) 2. (10 points) Consider the series (4.5* + 6). ko (a) When n = 3, write the series without summation notation, and find the sum. The series (when n = 3): The sum of the series (when n = 3): (b) Find the sum of the series for general n.
(10 points) This problem is related to Problem 9.15 in the text.
Consider the periodic function with period 16 given by
(10 points) This problem is related to Problem 9.15 in the text Consider the periodic function with period 16 given by if 8 t<-2 if 2 t4 if 4 t<7 if 7 t8 0 -6 f(t) = 6 0 Find the first 3 coefficients of the exponential Fourier Series for f(t), i.e., F(n) for n = -2, -1,0, 1,...
11. (10 points) - MATLAB ce of the alternating harmonic series, shown below: 1-2?--+ - 3 4 5 Use a loop to determine when the series has converged within a tolerance of 0.001. The animation should show how the value of the series changes as each successive term is added, resulting in a final
i 10 (1 point) Consider the series -. Let s, be the n-th partial sum; that is, in +9 10 Sn = i +9 Find 84 and so S4 S8 =
1. Consider the difference equation (1) Sn+2 - -8n+1Sn with initial conditions so = 0, 81 = 1 Let (x) n-0 denote the generating function of (sn) (a) Derive the fact that I++ = (x)f to show that (b) Use the generating function (x) r2+a+1 0 if n is a multiple of 3 1 if n is of the form 3j + 1 . -1 if n is of the form 3j 2 There are a number of ways to...
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