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MathSofiya
 2 years ago
Would this be correct?
\[f(x)=cos(\frac{(\pi x)}{2}\]
Use MacLaurin table
\[cosx=\sum_{n=0}^{\infty}(1)^n\frac{x^{2n}}{(2n)!}\]=\[1\frac{x^2}{2!}+\frac{x^4}{4!}frac{x^6}{6}\]
\[cos(\frac{(\pi x)}{2})=\sum_{n=0}^{\infty}(1)^n\frac{\frac{(\pi x)}{2}^{2n}}{(2n)!}\]=\[1\frac{\frac{(\pi x)}{2}^2}{2!}+\frac{\frac{(\pi x)}{2}^4}{4!}frac{\frac{(\pi x)}{2}^6}{6}\]
MathSofiya
 2 years ago
Would this be correct? \[f(x)=cos(\frac{(\pi x)}{2}\] Use MacLaurin table \[cosx=\sum_{n=0}^{\infty}(1)^n\frac{x^{2n}}{(2n)!}\]=\[1\frac{x^2}{2!}+\frac{x^4}{4!}frac{x^6}{6}\] \[cos(\frac{(\pi x)}{2})=\sum_{n=0}^{\infty}(1)^n\frac{\frac{(\pi x)}{2}^{2n}}{(2n)!}\]=\[1\frac{\frac{(\pi x)}{2}^2}{2!}+\frac{\frac{(\pi x)}{2}^4}{4!}frac{\frac{(\pi x)}{2}^6}{6}\]

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Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1\[ \Large \left(\frac{\pi x}{2}\right)^{2n} \]

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1The site is a bit dodgy for me today, it keeps reloading and kicking me out so I am not sure if I see the original equation correct.

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1sorry about that. The first line should read: \[f(x)=cos(\frac{\pi x}{2})\]

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1The second line was meant to be the macLaurin series for cos(x) that I found in my book. \[cosx=\sum_{n=0}^{\infty}(1)^n\frac{x^{2n}}{(2n)!}=1\frac{x^2}{2!}+\frac{x^4}{4!}\frac{x^6}{6!}\]

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1the final few lines are what I believe the answer should be. \[cos\left(\frac{\pi x}{2}\right)=\sum_{n=0}^{\infty}(1)^n\frac{\frac{(\pi x)}{2}^{2n}}{(2n)!}\]

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1Good, so you want to put wherever you see an x, you want to put the following: \[ \Large \left( \frac{\pi x}{2} \right) \] right? because that is your new 'x' which you can substitute into the given equation.

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1yeah I think so. That would make. \[1\frac{\left(\frac{\pi x}{2}\right)^2}{2!}+\frac{\left(\frac{\pi x}{2}\right)^4}{4!}\frac{\left(\frac{\pi x}{2}\right)^6}{6!}\]

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1yes, exactly! I was confused first, because the way you did \(\LaTeX\) it in your original post it looked like you would take the Exponent \(2n\) only in consideration for the numerator, but you also have to take it in consideration for your denominator  just like you did!

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1Thank you! It's kinda difficult typing latex blindly in the Question box to the left.

Spacelimbus
 2 years ago
Best ResponseYou've already chosen the best response.1No problem, you did it all right then, I was just making sure that you noticed that (: And I agree, there should at least be a preview function of the post!
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