Mathematical Analysis - Continuity

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Homework Statement



attachment.php?attachmentid=46322&stc=1&d=1334638231.png


Homework Equations


The Attempt at a Solution



Basically the first part of the question asks to prove the binomial theorem through induction which I've done.

I'm basically lost as to how to even attempt these questions, I'm not asking for answers as I need to know this stuff for exams and other courses.

Can anyone point me to a place where I can find similar style of questions with an explanation on the theory on how to do them?

We've only been shown in lectures on how to show continuity through epsilon-delta arguments?
 

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Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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