Limit of an Arithmetic Series: Solving for the Limit as n Approaches Infinity

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Limn→∞ (n2/1+5+9+...+(4n-3))
 
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Since you apparently didn't take VietDao's suggestion, I'll tell you the answer is 1/2 and let you figure out if it's correct or not.
 
I have no idea how to do it...so I am asking to give me a clue to this problem!
 
The denominator is an arithmetic series, which sums to 2n2 - n. Therefore the limit is 1/2.
 

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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