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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?
 one year ago
 one year ago
\[f(x)=cosh(x)=1+0+\frac{x^2}{2!}+0+\frac{x^4}{4!}+....\] 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?
 one year ago
 one year ago

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MathSofiyaBest 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
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
these are even values of the exponent, so we use the other formula with the 2n
 one year ago

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

TuringTestBest 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
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
so just take out the dots lol
 one year ago

MathSofiyaBest ResponseYou've already chosen the best response.1
oooh because their just zero's and one's ?
 one year ago

TuringTestBest 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
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
you do not need to represent the 0 terms
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
you only need to represent the resulting series
 one year ago

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

TuringTestBest 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
 one year ago

TuringTestBest ResponseYou've already chosen the best response.1
that agrees with your results doesn't it?
 one year ago

TuringTestBest 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
 one year ago

MathSofiyaBest 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!
 one year ago
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