How Many Ways Can a Number Be Represented as an Arithmetic Series Sum?

Natasha1
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I have been asked to write up a 20 page report on the following...

For example 2 + 3 + 4 = 9 or 7 + 8 + 9 +10 = 34

Investigate this theme? (Hints from my teacher how many ways can a number be thus obtained? Could you specify which numbers can be done in just one way, two ways, etc. Use the arithmetic series sum formula)

What's this all about? heeeeeeeeeeeeeeeeeeeelp please :confused:

Any further thoughts welcome ;)
 
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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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