[SOLVED] Convergence of a series

I have a question that I can't do...can anybody help me?

Investigate the convergence of the series (in the complex plane) for difference values of a and b:

Generalise your solution by determining what constraints are required on the values of a and b, so as to guarantee the convergence of the series?



Thanks if you can help.

assuminf a and b are both real

But I thought a + bi is a complex number.
i.e. b is not real.

Quote:

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Originally Posted by Bucephalus

But I thought a + bi is a complex number.
i.e. b is not real.

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in the form a + bi, both a and b are real. that is generally how complex numbers are defined. we get a complex number because there is an "i" attached to the real number b

So the assumption was that a and b are real numbers i.e.
it is not of the form a + (c +di)i
that's what I now understand of that that assumption is assuming.
Is this correct?

Quote:

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Originally Posted by Bucephalus

So the assumption was that a and b are real numbers i.e.
it is not of the form a + (c +di)i
that's what I now understand of that that assumption is assuming.
Is this correct?

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correct. a and b are considered to be real unless otherwise stated.

and it would not be otherwise stated, since even a + (c + di)i can be rewritten in the form a + bi

Because I thought that the condition for geometric series convergence is

|r| < 1 for geomtric series



thanks.

Quote:

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Originally Posted by Bucephalus

Because I thought that the condition for geometric series convergence is

|r| < 1 for geomtric series



thanks.

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this you should answer !!!

Thanks.