## 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

1. MathSofiya Group Title

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. TuringTest Group Title

these are even values of the exponent, so we use the other formula with the 2n

3. MathSofiya Group Title

ooops

4. MathSofiya Group Title

$\sum_{n=0}^{\infty} \frac{...x^{(2n)}}{(2n)!}$

5. TuringTest Group Title

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

6. TuringTest Group Title

so just take out the dots lol

7. MathSofiya Group Title

oooh because their just zero's and one's ?

8. TuringTest Group Title

yup try out some values of n plug in n=0 n=1 n=2 etc. you will see you get your series

9. MathSofiya Group Title

check out my table

10. TuringTest Group Title

you do not need to represent the 0 terms

11. TuringTest Group Title

you only need to represent the resulting series

12. MathSofiya Group Title

$f(x)=cosh(x)=1+\frac{x^2}{2!}+\frac{x^4}{4!}+....$ ?

13. TuringTest Group Title

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

14. TuringTest Group Title

that agrees with your results doesn't it?

15. MathSofiya Group Title

makes sense

16. TuringTest Group Title

so there you have it$\cosh x=\sum_{n=0}^\infty{x^{2n}\over (2n)!}$a nice, simple series representation

17. MathSofiya Group Title

$f(x)=cosh(x)=1+\frac{x^2}{2!}+\frac{x^4}{4!}+....=\sum_{n=0}^{\infty} \frac{x^{(2n)}}{(2n)!}$ final answer. Very good, THankss!

18. TuringTest Group Title

welcome!