收敛半径 R = lim<n→∞>a<n>/a<n+1>
= lim<n→∞>(2^n+3^n)·(n+1)/{n·[2^(n+1)+3^(n+1)]}
= lim<n→∞>[(n+1)/n]·(2^n+3^n)/[2^(n+1)+3^(n+1)], 后者分子分母同除以 3^n
= lim<n→∞>(1+1/n)·[(2/3)^n+1]/[2(2/3)^n+3] = 1/3
x = -1/3 时,级数变为 ∑<n=1,∞> (-1)^n(2^n+3^n)/(n·3^n)
= ∑<n=1,∞> (-1)^n[(2/3)^n+1]/n 收敛;
x = 1/3 时,级数变为 ∑<n=1,∞> (2^n+3^n)/(n·3^n)
= ∑<n=1,∞> [(2/3)^n+1]/n 发散。
故原级数收敛域是 x∈[-1/3, 1/3).
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