The function f(x) = 3/1 + 100x2 is represented as a power series . Find the firs

Question

The function f(x) = 3/1 + 100x2 is represented as a power series . Find the first few coefficients in the power series. c0 = c1 = c2 = c3 = c4 = Find the radius of convergence R of the series. R = . The function f(x) = ln(2 - x) is represented as a power series . Find the first few coefficients in the power series. c0 = c1 = c2 = c3 = c4 = Find the radius of convergence R of the series. R = The function f(x) = 9x ln(1 + 2x) is represented as a power series .Find the FOLLOWING coefficients in the power series. c0 = c1 = c2 = c3 = c4 = Find the radius of convergence R of the series. R = .

Explanation / Answer

f(x) = 3/(1+100x^2) = 3*(1+100x^2)^(-1) = 3*[1 - 100x^2 + 10000x^2 -10^6 * x^6 + .....]

=> C0 = 3

C1 = 0

C2 = -300

C3 = 0

C4 = 30000

R = 100

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