设n∈N*,(2x+1)^n的展开式各项系数之和为an,(3x+1)^n展开式的二项式系数之和为bn,求limn→+∞(2an+3bn)/(an+1*bn+1)的值
问题描述:
设n∈N*,(2x+1)^n的展开式各项系数之和为an,(3x+1)^n展开式的二项式系数之和为bn,求limn→+∞(2an+3bn)/(an+1*bn+1)的值
答
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•...