When working on this problem I am absolutely stumped on what to do. This is because every other coefficient is zero but no part of the problem suggests this is the case.
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To find the radius of convergence this problem needs the same trick I used in class on Wednesday to talk about the Taylor series of cos(x). You should write the sum as ∑c_{2n}(x^2)^n, which you can do because all of the coefficients c_n with n an odd integer are zero, so you can just leave them out. Then the ratio test looks at the limit of (| c_{2n+2} x^{2n+2} |)/(| c_{2n} x^{2n} |).
To find the radius of convergence this problem needs the same trick I used in class on Wednesday to talk about the Taylor series of cos(x). You should write the sum as ∑c_{2n}(x^2)^n, which you can do because all of the coefficients c_n with n an odd integer are zero, so you can just leave them out. Then the ratio test looks at the limit of (| c_{2n+2} x^{2n+2} |)/(| c_{2n} x^{2n} |).
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