Hey All,
Can someone check if I have done this right. Thank you
find the range of values for x for which:
____∞
s = ∑ 9^nx^{2n} / n^3
__n=1
Un + 1 = 9^n.9.x^{2n}.x^2 / n^3 + 3n^2 + 3n + 1
(Un+1)/(Un)= 9^n.9.x^{2n}.x^2 / n^3 + 3n^2 + 3n + 1 . n^3 / 9^n + x^{2n}
simplifying
9x^2.n^3 / n^3 + 3n^2 + 3n + 1
dividing n^3
9x^2 / 1 + 3/n + 3n^2 + 1/n^3
n→1
9x^2 / 8