(b) Using the Root Test, or otherwise, determine the radius of convergence of the power series (n4-5n³) (3n²-8n4)n (2+i)". State the test that you are using and justify all of your steps.
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- What is the radius of convergence for n2/(4n+3n)a. Find a real root of the equation e\power{x}tanx=1by using iteration method and also apply Aitken's Δ\power{2} -process to acceleratethe convergence. b Find the value of e\power{-1} where e=2.718 by using newton raphson.(a) Find a real root of the equation e^xtanx=1 by using iteration method and also apply Aitken's del^2 -process to accelerate the convergence. (b) FInd the value of the e^-1 when e=2.718 by using newton raphason method.
- To find the unique solution p^∗ ∈ [0, 1] of the equation x^3 + 6x^2 − 4 = 0, rewrite the equation in the fixed-point form x = g(x) with two different choices of g, such that the sequence {pn} from the fixed-point iteration pn = g(pn−1) is expected to converge to p^∗ when p0 is sufficiently close to p^∗(but not equal to p^∗). Explain why your choices of g would work.Find the radius of convergence and the interval of convergence. ∑k=0∞(x−3)k2kFind the first 4 non-zero terms of (1+3x)^(1/4) centered at x=0. what is the radius of the convergence?
- Find the radius and the interval of convergence of ∑∞n=1 (3^n*(2-x)^n)/(n+1)I had tried Xn=(-1)^nbut since 2((-1)^n)^n =2(-1)^(n^2) (which is not always 1) it doesn't converge to some real number.Find a power series for the function, centered at C and determine the interval of convergence (function is h(x) and C = 0).h(x)=1/(1-5x) Also see the attached picture of the problem.