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Please do question 13.
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- Calc & Anal Geometry II Use any appropriate series test to determine whether the series converges or diverges ∞ ∑ cos((2n+1)π/2 n=1Solve the IVP by a power series showing details of your work. Find the value of the sum at x1 to 6 significant figures (6S) (x2 + 2) y” + 3 x y’ - y = 0 y (0) = 1 y’ (0) = 1 x1 = 0.5Solve using a Power Series Centered at 0. Express your answer in the form y = c0(First three non-zero terms of Series1+ · · ·)+c1(First 3 non-zero terms of Series2+ · · ·). You do not have to simplify/multiply the coefficients y'' + x2y' = 0
- The ecuation (1) has two fundamental solutions y1, y2. Find the first three terms of each power series expansion centered at 0 of y1, y2.(a) Find a power series representation for f(y) =(y^2)/(b+y^3), b >0. use Σ notation, with nothing in front of (or outside of) the Σ, with only one factor for each variable or constant, and no fractions within fractions. (b) State the radius of convergence of your power seriesVv Express the function f(x) = a ln(1+cx) in power series form. Then evaluate the series at x = 0.127 using the first five terms of the series if a = 15.6 and c = 2.
- Solution is not complete. What is the combined power series of the function at zero?Series(a) Find the exact value that X∞n=1√n −√n + 2 converges to, or else concludethat the series diverges.(b) Determine whetherX∞n=1(−1)n· n2 + 2(n − 1)! converges absolutely, converges conditionally, or diverges.decide if the given statement is true or false,and give a brief justification for your answer.If true, you can quote a relevant definition or theorem .If false,provide an example,illustration,or brief explanation of why the statement is false.Q.)`A power series solution to y′′+ p(x)y′+q(x) = 0 centered at an ordinary point x =x0 always exists and has a positive radius of convergence.
- pls provide a detailed solution using geometric series test and integral test find out if the series converge or divergeDetermine the sum of the series if possible. (If the series diverges, enter 'infinity', '-infinity' or 'dne' as appropriate.) (Hint: try breaking the summands up partial fractions-style.) I got my answer incorrect. Can anyone do it correctly?making a Series Converge:- In the given equation as folows, find allvalues of x for which the series converges. For these values ofx, write the sum of the series as a function of x:- see the equation as attached here