Top Homework Threads: Recognizing Exceptional Question Presentations

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Gokul43201
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Every now and then, this forum has the rare and satisfying experience of hosting a well presented homework thread - a thread where the member seeking help has chosen a title well, written out the original question completely, provided sources and diagrams if required, explained their background and thought process, as well as described the nature of the help needed. Such threads are a pleasure to read and help out with.

In this sticky, the Homework Helpers recognize, congratulate and thank the members who take the care that is necessary to effectively present their questions and show the effort they have made towards answering them.

The following list of members/threads will be updated as and when noteworthy threads catch the attention of the Homework Helpers. We can only hope that more and more posters follow these examples, and that threads like those below become the norm, rather than the exception.

And the authors of the Best Homework Threads are (recent inductees at the top):

thiago_j

app

mike412

VinnyCee

danago

Tokipin
 
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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