Sigma Notation and string of numbers

AI Thread Summary
The discussion centers on converting a sequence of numbers (3, 6, 12, 24, 48, 96) into Sigma Notation. The correct representation is identified as the sum from k=0 to 5 of 3 multiplied by 2 raised to the power of k. There is some confusion about what constitutes the "correct Sigma Notation equation." The participant expresses gratitude for the clarification, indicating that this solution will help them assist their son. Overall, the thread highlights the process of understanding and applying Sigma Notation to a specific numerical sequence.
Old Math Dad
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Trying to help my son & I am in Waaaaay over my head.

He has a string of numbers and needs to come up with the correct Sigma Notation equation.

3, 6, 12, 24, 48, 96
 
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3\ +\ 6\ +\ 12\ +\ 24\ +\ 48\ +\ 96\ =\ \sum _{k=0}^53\cdot2^k

Is that what you wanted? Given a sequence of six numbers, it's not clear what you even mean by "the correct Sigma Notation equation".
 
Bless Your Pointed Little Head.
I will look like a hero now.
Thank You VERY MUCH.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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