What is the formula for calculating the sum of consecutive integers?

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Homework Statement



1+2+3...+n


Homework Equations



count the sum.


The Attempt at a Solution



it's such an easy sum to count but i just want to make sure.

S_{n}=\frac{n}{2}(a_{1}+a_{n})


S_{n}=\frac{n}{2}(1+n)


S_{n}=\frac{n+n^{2}}{2}
 
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Correct. Hope your anxiety is eased
 
Lol its too simple idk why my teacher would give us something so simple I thought there would be a trick or something.
 

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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