Product Notation: Expressing Prod_{n=1}^k a_i

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The discussion focuses on expressing products in terms of the notation \prod_{n=1}^k a_i, specifically addressing the expression \prod_{n=1}^k k a_i. It is clarified that the constant k cannot simply be factored out; instead, it results in k^k when considering the product. Additionally, a question arises about expressing the product \prod_{n=1}^k a_i without a k present, leading to confusion on how to relate it to k. The participants emphasize the importance of understanding the properties of products in this context. Overall, the conversation highlights the nuances of manipulating product notation in mathematical expressions.
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I have a quick question. In my book, there is a question that says to express each of the following products in terms of \prod_{n=1}^\k\a{i}, where k is constant. Now, my question is this: \prod_{n=1}^\k\ka_i. Would i just pull the k out becuase it is only a constant and move that to in front of the product? This almost looks like a property that is similar with summation, but I think I have to do more than simply move the k. Anyone understand/assist? Thank you all. I hope everyone can understand my LaTeX. The number atop the product is supposed to be k, NOT 1. Damn latex. :devil:
 
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no, you multiply by k every time, meaning that outside it would turn into k^k
 
Ok, so on the outside of the product, I would have k^k=product a_i?

I have another question that just blows my mind:

The product is the same, but it reads ia_i. There is no k in the question, how am I to write this in terms of k??
 

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