Recent content by thanksie037

thanks! I finally got it. i appreiate your help. cool problem.

sorry, the problem specifies artanh . . . solving for e^x won't give me the same properties that using z implies (since z = xi + y)

Homework Statement prove: arctanh(z) = 1/2 ln( (1+z)/(1-z) ) Homework Equations cosh z = (ez + e-z)/2 sinh z = (ez - e-z)/2 ez = ex + iy = ex(cosy + siniy) The Attempt at a Solution cosh z / sin hz = ez+e-z/ez-e-z

I'm sorry that was a typo. Should I just expand both was like you would ex? how about the 1/x part?

Homework Statement power series expansion of: ((cosh x)/(sinh x)) - (1/x) Homework Equations cosh x = (1/2)(ex + e-x) sinh x = (1/2)(ex - e-x) The Attempt at a Solution what i have so far: I simplified the first part of the eq to read : e2x-1 e2x-1 now I am stuck...

yeah I was going to say that's what I got... lots of thanks to gab, I would have put my work in here but I don't know how to use this forum very well.

That makes sense. Thanks for all your help. One more unrelated quick question: do the series n/(n+1) and n^2/(n^2+1)converge or diverge?

and how do i even find the sum of this series. i only know how to find a sum of a geometric series...i don't know how to deal with the factorial

sorry i was using that first one. i was confused as to what you meant with cos nx. using the second one makes a lot more sense. are you saying i should: cos n(theta) = (e^ni(theta) +e^-ni(theta))/2

Do you mean: x^ni=cos nx + sin nx?

would x= cosnx? is there a property for cosine where (cos x)^n=cos nx ?

Hi, Yes we can compare it to known series. I've tried a comparison with the harmonic series and the expansion for e^x looks promising. I'm just not sure how to get started.

Homework Statement Find the sum of the series s(x) = 1 +cos(x)+ (cos2x)/2!+(cos3x)/3!... Homework Equations The Attempt at a Solution

Homework Statement Find the sum of the series s(x) = 1 +cos(x)+ (cos2x)/2!+(cos3x)/3!... Homework Equations The Attempt at a Solution i'm miserable at series. help?

do i need to find any more critical points? or will that suffice.. thank you for your help, by the way. your explanations have been clear, concise and beyond enlightening.