Representing 5/(1+9x^2) as a power series and its coeffecients?

115 Views Asked by At

I have the equation f(x) 5/(1+9x^2) and to represent it as a power series I switch it to 5/(1-(-9x^2)) ---> 5∑(-9x^2)^n, my range of integration is correct but my first few coefficients of the power series I get are

C0: 5(-9x^2)^0 = 5(1) = 5 (this one is the only one I got correct)

C1: 5(-9x^2)^1 = 5(-9x^2) = -45x^2 -> -45

C2: -> 405

C3: -> -3645

C4: -> 32805

Am I making a stupid arithmatic mistake or is there a bigger problem and I just lucked out in getting the first one and range correct?