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MathSofiya
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\[f(x)=cosh(x)=1+0+\frac{x^2}{2!}+0+\frac{x^4}{4!}+....\]
Maclaurin's
I'm having some trouble writing this in summation form
\[\sum_{n=0}^{\infty} \frac{f^(0)}{n!}x^(n)\]
I know that:
All even #'s can be written as 2n
All odd #'s can be written as 2n+1
\[\sum_{n=0}^{\infty} \frac{...x^{(2n+1)}}{(2n+1)!}\] I think?
so how do I write the \[f^n (0)\] correctly?
 2 years ago
 2 years ago
MathSofiya Group Title
\[f(x)=cosh(x)=1+0+\frac{x^2}{2!}+0+\frac{x^4}{4!}+....\] Maclaurin's I'm having some trouble writing this in summation form \[\sum_{n=0}^{\infty} \frac{f^(0)}{n!}x^(n)\] I know that: All even #'s can be written as 2n All odd #'s can be written as 2n+1 \[\sum_{n=0}^{\infty} \frac{...x^{(2n+1)}}{(2n+1)!}\] I think? so how do I write the \[f^n (0)\] correctly?
 2 years ago
 2 years ago

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MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
here is my table n f^n x f^n 0 0 coshx 1 1 sinhx 0 2 coshx 1 3 sinhx 0 4 coshx 1
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
these are even values of the exponent, so we use the other formula with the 2n
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
\[\sum_{n=0}^{\infty} \frac{...x^{(2n)}}{(2n)!}\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
besides that you have written all there is to the series; there is nothing in front of each term that you are missing in your sigma notation
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
so just take out the dots lol
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
oooh because their just zero's and one's ?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
yup try out some values of n plug in n=0 n=1 n=2 etc. you will see you get your series
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
check out my table
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
you do not need to represent the 0 terms
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
you only need to represent the resulting series
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
\[f(x)=cosh(x)=1+\frac{x^2}{2!}+\frac{x^4}{4!}+....\] ?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
your table is for the coefficients, and it should tell you that you are keeping only even exponents, hence you use 2n for the exponent and factorial
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
that agrees with your results doesn't it?
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
makes sense
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
so there you have it\[\cosh x=\sum_{n=0}^\infty{x^{2n}\over (2n)!}\]a nice, simple series representation
 2 years ago

MathSofiya Group TitleBest ResponseYou've already chosen the best response.1
\[f(x)=cosh(x)=1+\frac{x^2}{2!}+\frac{x^4}{4!}+....=\sum_{n=0}^{\infty} \frac{x^{(2n)}}{(2n)!}\] final answer. Very good, THankss!
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.1
welcome!
 2 years ago
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