Solving Homework Problem: ln and e Inverse Process

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Homework Statement



http://img513.imageshack.us/img513/2687/problem15001.jpg

Homework Equations



I know the answer is e but i forgat how to do the lny=xln(1+1/n) and then I solve an get an e because ln and e are inverse but i forgot the process can you please show me the process

The Attempt at a Solution

 
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at the stage

\stackrel{lim}{n \rightarrow \infty}, ln(y) = n.ln(1+1/n)

the limit is indeterminant 0 * infinity, so can you re-write it and use L'Hopitals rule...?
 

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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