偶数乘积与奇数乘积比值的极限
来源:百度知道 编辑:UC知道 时间:2024/06/28 02:21:25
(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
分子分母同时除以n!,化简后为lim2^n/2^n=1