I'm trying to figure out what the summation notation of

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SUMMARY

The discussion centers on converting the expression (1-x1)^θ * (1-x2)^θ * ...(1-xn)^θ into summation notation. Participants clarify that the original expression represents a product rather than a sum. To express this mathematically, the product notation can be utilized, specifically using the product symbol: \prod_{k=1}^n (1-xk)^θ. This notation effectively captures the multiplication of the terms across the specified range.

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stevenham
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I'm trying to figure out what the summation notation of

(1-x1)^θ * (1-x2)^θ * ...(1-xn)^θ would be for summation

I know I need to convert this to a summation notation in order to solve my problem, but I can't figure out how to convert it. Any help will be appreciated.
 
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stevenham said:
I'm trying to figure out what the summation notation of

(1-x1)^θ * (1-x2)^θ * ...(1-xn)^θ would be for summation

I know I need to convert this to a summation notation in order to solve my problem, but I can't figure out how to convert it. Any help will be appreciated.

As you have written this, it's not a sum - it's a product. In a summation, the terms are added. In a product, the factors are multiplied.

For example, you can write 12*22*32*...*n2 as a product like this:
\prod_{k=1}^n n^2
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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