Recent content by chouse12

I see now the mistake I was making with the ratio test...thanks for the help. I can get the other two parts of the problem pretty easily now. Thanks again for all the help, couldn't have done it without you guys.

Just another quick question...I need to find the interval of convergence for this series. I set up the ratio test and I think I must be doing it wrong because I am getting convergence for all real values of x but in my textbook it says the binomial series only converges from -1 to 1. Here is...

Oh that clears everything up...Thank you so much for the help.

lanedance, that is almost correct. That gives coefficients of 1, 2/2, 24/8, 720/48... which simplify, to 1, 1, 3, 15... The denominator is correct but the numerator is not. The coefficients should be 1, 1/2, 3/8, 15/48... so if the bottom term was squared then it would be correct. So any ideas...

Dick, from Tiny-Tim's answer, I notice that it is just (2n-1)! simplified into terms with single factorials (i.e. (2n-1)!=(2n)!/2nn!) but instead of in the denominator 2nn!, it is that quantity squared (22n(n!)2). Does this make the terms in the denominator the even integers?

Dick, I did not know about double factorials or other multiple factorials before so thanks for that. However, how do I make the top odd and the bottom even? On one website I looked at, it just has n! as a piecewise term, making the terms all even for n>0 and even and all odd for n>0 and odd. Or...

Ok, I messed around with it a little more and ended up with this: 1+ (1/2)(x) + ((1)(3)/(2)(4))x^2 + ((1)(3)(5)/(2)(4)(6))x^3+... So the coefficients on each term is with consecutive odd integers in the numerator, always multiplying by the next integer in the next term, and consecutive even...

tiny-tim, Thanks for the welcome and the hint. The main problem for me seems to be getting the first series though.. lanedance, so far I have the series expressed as (-1)^0/2^0/0!(-x)^0 + (((-1)/2^1)/1!)(-x)^1+(((-1)(-3)/2^2)/2!)(-x)^2+(((-1)(-3)(-5)/2^3)/1!)(-x)^3+...+...

Homework Statement 1. Find a power series for (1-x)^(-1/2) 2. Find a power series for (1-x^2)^(-1/2) 3. Find a power series for arcsin(x) Homework Equations Binomial series, (1+x)^k= 1 + kx + k(k-1)x^2/2!+ k(k-1)(k-2)x^3/3!+... The Attempt at a Solution for 1., I have 1+ (-1/2)(-x) +...