Largest open interval of convergence for the power series about c= 0 representing function f(x)= 2/(4x^2 + 9)?

all the back of the book solutions....











a. (-1/6, 1/6)





b. (-1/4, 1/4)





c. (-1/3, 1/3)





d. (-1/2, 1/2)





e. (-1, 1)





f. (-3/2, 3/2)





g. (-2, 2)





h. (-3, 3)





i. (-4, 4)





j. none of these

Largest open interval of convergence for the power series about c= 0 representing function f(x)= 2/(4x^2 + 9)?
f(x) = (2/9) /( 1+(2x/3)^2)


= (2/9)( 1 - (2x/3)^2 + (2x/3)^4 - (2x/3)^6 ...)


alternating series


converges if (2x/3)^2 %26lt; 1


i.e. |x|%26lt;3/2


so answer f... (-3/2, 3/2)