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- If C(x)=∞∑n=0 2n/4n^2+1 x^2n and S(x)= ∞∑n=0 2n+1/(2n+1)^2+1 x^2n+1, find the power series of C(x)−S(x)C(x)-S(x).If f(x) = 3 n = 0 - and g(x) = (-1)^x, find the power series of(f(x) + g(x)) and of 1⁄(f(x) − g(x)). n! n = 0 1 / (f(x) + g(x)) = Σ n = 0 ((x)6 – (x)) = n = 0The function f(x)=3xarctan(6x) is represented as a power series (image) Find the first few coefficients in the power series.
- 20 10. Let f(x)= 1+20x (a) Express this function as a power series. (b) Let g(x) = In(1+ 20x). Express this function as a power series using your answer from part (a).If y = E=0 anx" = ao + a1x + a2x² + ... is the series solution of y'-y = 3x2, then the coefficient of x³ in the series solution is ao+6 (a) 6. ao-6 (b) 6. ao+3 (c) 6. (d) 40+6 6. 1 (e)ao +13.) Find a power series for the function f(x) = = 5 2-6x3*