Find the values of x for which the series ∞Σ(n=1) (3^n)/(x^n) converges. Find the sum for those values of x.?

1.
(1)
a_n = 3^n / x^n = (3/x)^n
a_n+1 / a_n = (3/x)^(n+1) / (3/x)^n = 3/x
｜3/x｜< 1 即收斂
故 ｜x｜> 3
x > 3 or x < - 3 ..... Ans

(2)
此級數為等比級數, 公比 = 3/x
S
= (3/x) / [ 1 - 3/x ]
= (3/x) / [ ( x - 3 )/x ]
= 3 / ( x - 3 ) ..... Ans