Help me fast so that I will give good rating....... 4. (a) Find the limits if it exists, if it does not explain why.(1) lim ("(ii) limn 00(b) (i) Let R be the radius of convergence of the power series an(z – z.)" and suppose thatn=0ant1limn 00L exists, for some real number L, show that R = }.%3Dan(ii) Find the radius of convergence of the seriesE(z - ni)", hence, find the region aboutz = ni where the series converges.(c) Let z and w be none zero complex numbers. Prove that | z+ w - | z – w = 4Re(zw).

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Math

Advanced Math

the limits if it exists, if it does not explain why. (1) lim ()" (ii) lim

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 49E

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Help me fast so that I will give good rating.......

4. (a) Find the limits if it exists, if it does not explain why.
(1) lim ("
(ii) lim
n 00
(b) (i) Let R be the radius of convergence of the power series an(z – z.)" and suppose that
n=0
ant1
lim
n 00
L exists, for some real number L, show that R = }.
%3D
an
(ii) Find the radius of convergence of the series
E(z - ni)", hence, find the region about
z = ni where the series converges.
(c) Let z and w be none zero complex numbers. Prove that | z+ w - | z – w = 4Re(zw).

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