complex variables 22. Prove that the series log (1 + a) and ma, converge absolutely in...

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22. Prove that the series log (1 + a) and ma, converge absolutely in a simulta- neous manner. Suggestion. This is an immediat

complex variables

Answer 1

Answer #1

We know the following theorem: an If lim = 1 (finite and nonzero) is 1, then it true that both the nu bn series 2n=1 an, In=1

= lim 2-0 1/(1+z) 1 = 1 Thus if In=1 an converges then an → 0 and so if we write z = an, then the above limit is same as log(

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Answer 2

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