Finding Limit for Equation: Step-by-Step Guide

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To find the limit for the given equation, factoring the expression (1-1/k²) is essential for simplification. The user suggests using the difference of squares formula, (a² - b²) = (a-b)(a+b), to aid in the cancellation process. By substituting values of k and writing down the initial terms, the cancellation becomes evident. This step-by-step approach helps clarify the limit calculation. Understanding these techniques is crucial for successfully finding limits in similar equations.
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I'm trying to find a limit for this equation:

http://www.formulabin.com/formula/63540850c94efe3e011e283862cc0939

Now I understand I can factor (1-1/k^2) and look for cancellation, but I just can't figure out how to do that in this case.
 
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Do the (a² - b²) = (a-b)(a+b) bit, then substitute in values of k and write down the first few terms multiplied together.
You will see the cancelling out.
 
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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