令x=1由二项式定理可得an=3ⁿ,（3x+1﹚ⁿ展开式的二项式系数之和bn=2ⁿ∴ limn→∞2an+3bn/an+1bn+1= limn→∞2•3ⁿ+3•2ⁿ/3﹙ⁿ+1﹚+2﹙ⁿ+1﹚= limn→∞2+3•...