Convergence/Divergence of a Geometric series with a Factorial

sikrut
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Homework Statement



Determine if the sequence {an} below converges or diverges. Find the limit of each convergent sequence

an = n!/nn

Hint: Compare with 1/n .

Find the limit of the sequence {an} if it converges.


I missed the lesson on factorials, and the book is useless. Sorry if this seems rather simple...
 
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Factorial is n! = 1*2*3*..*n, and n^n = n*n*n*...*n. Which one is bigger now?
 

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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