Test the series for convergence or divergence using the Alternating Series Test. (-1)" - 1 Σ 4 + 7n n = 1 Identify b, Evaluate the following limit. lim b. 'n Since lim b ? O and b, +1? v b, for all n, ---Select---
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- Find the Taylor series for f (x) = 1/x centered at a = −3. Also, find the interval ofconvergence. (Find R and the interval of convergence) Thank you. In problems determining series convergence or divergence, include:• The name of the convergence test or the definition used,• work to show that the test conditions have been met or work to apply thedefinition,• and a conclusion statement about convergence or divergence.determine the Taylor series about the point x0 for the given function. Also determine the radius of convergence of the series. 10.x2, x0 = −1Find a power series representing an antiderivative of f(x) = e-(x^4) Use the power series to evaluate lim as x--> 0 of (e-(x^4) + x4 - 1) / x8
- find1) the power series using transformations of the types A-G of theknown power series of the corresponding elementary function,2) the radius of convergence,3) the interval of convergence,4) the 7-th derivative of f(x) at x = 0.Find a power series representation for the function. Determine the interval of convergence. f(x) = 1/(6+x)Does the series from 3 to infinity for (ln(n))/(ln(ln(n)) converge conditionally, absolutely or diverge. Please use one of the following test to demonstrate the solution. If possible use more the one test Integral Test Comparison Test Limit Comparison Test Alternating Series Test Ratio Test Root Test Please show steps in detail Thank you