Σ(-1). , where [.] denotes the greatest integer function, is [cos n] (n + 1)² n=1 O absolutely convergent O divergent conditionally convergent convergent
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![Σ(-1). , where [.] denotes the greatest integer function, is
[cos n]
(n + 1)²
n=1
O absolutely convergent
O divergent
conditionally convergent
convergent](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F108f8a6c-2955-46fa-b885-667817ffe50f%2F5f7351d1-66b0-404a-a16a-0c116ba7aaf6%2Ff7pg7uj_processed.png&w=3840&q=75)
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- Show that En=2 logn 1 Prove that Σn(n+1) diverges to ∞. - 1. (hint: 1 n(n+1) = n 1/1). n+1Let f(e) = { , 1 ISI< 2n Find the Fourier series of f (x) over the interval [0,27]1. Find the F.S. expansion of f(x) = x n = x < XIf En and S, is its n-th partial sum, find: 3 2. (a) lim cos(an) (b) lim S. ||Q(A). Let {fn(x)}-1=3: be a sequence of functions + (x – 2)* S. n=1 defined over [2,3]. Show that: (a) fn(x) is meaurable and monotonic increasing for all n.5. s) Find the Fourier series of the following function and discuss its convergence on the interval -Y, 1< x < 0 f(r) = x. 03. Show that II (1+22) is absolute convergent if and only if |z| < 1. Show k=0 that the product converges to 4. Show that 1+sin( is absolute and uniform convergent for all 2. k=0 5. Show that Res(T(2);-n) = (-1)" n!1.) Find the Fourier series for the function f(t) = (1,-4 < t ≤0 2,05. Expand the following function in Fourier series where f(x) = { show that f(x): = + 22-1 [(-1)^-1 nπ ·cos nxX- [1 when -16.5 Use the series for f(x) = on [x| < 1 to construct a series for (1 – x)(x – 2)' Determine the interval of convergence.Determine whether the Fourier series of the following functions converge uniformly or not. f(x) = x + |x|, −1 < x < 1; Solve using power and series (Fourier)(please) Note: Calculate ao ,an and bn Answer: Not converge6.2.8Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,