来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/05/12 17:31:16
偶数乘积与奇数乘积比值的极限
(2×4×6×……×2n)/(3×5×7×……×(2n+1))—>?(n->∞)
2/3 < 3/4,
4/5 < 5/6,...
2n/(2n+1) < (2n+1)/(2n+2)..
So:
((2×4×6×……×2n)/(3×5×7×……×(2n+1)))^2
< (2/3)* (3/4)*(4/5)*(5/6)*...*((2n)/(2n+1))*((2n+1)/(2n+2))
= 2/(2n+2)=1/(n+1)---> 0