n趋向正无穷时,[(2n-1)!!⼀(2n!!)]的极限是多少?

2025-02-02 02:56:09
推荐回答(1个)
回答1:

设 u(n)=[(2n-1)!!/(2n!!)] =1/2 * 3/4 * 5/6 * ...... * (2n-1)/(2n)
x(n)= 2/3 * 4/5 * 6/7 *......* (2n)/(2n+1)
u(n)*u(n) < u(n)*x(n) = 1/(2n+1)
0夹挤准则,
=> Limit [u(n),n->∞] =0