求lim(1-1/4)(1-1/9).(1-1/n^2) n趋于无穷

来源：学生作业帮助网编辑：六六作业网时间：2025/02/01 06:59:09

求lim(1-1/4)(1-1/9).(1-1/n^2)n趋于无穷求lim(1-1/4)(1-1/9).(1-1/n^2)n趋于无穷求lim(1-1/4)(1-1/9).(1-1/n^2)n趋于无穷1

求lim(1-1/4)(1-1/9).(1-1/n^2) n趋于无穷
求lim(1-1/4)(1-1/9).(1-1/n^2) n趋于无穷

求lim(1-1/4)(1-1/9).(1-1/n^2) n趋于无穷
1-1/n^2=(n-1)/n*(n+1)/n
(1-1/4)(1-1/9).(1-1/n^2)
=1/2*3/2*2/3*4/3*3/4*5/4*……*(n-1)/n*(n+1)/n 中间项约去
＝(n+1)/2n
lim(1-1/4)(1-1/9).(1-1/n^2) n趋于无穷
=1/2

1-1/n^2=(n^2-1)/n^2=(n+1)(n-1)/n^2
所以
（1-1/4)(1-1/9)....(1-1/n^2)
=[1*3/2/2]*[2*4/3/3]*[3*5/4/4]*.....*[(n-1)(n+1)/n/n]
=1/2*(n+1)/n
->1/2（n->无穷)

lim(2an+4bn)=1 lim(3an-bn)=2 求lim(an+bn) lim(2an+4bn)=1 lim(3an-bn)=2 求lim(an+bn) {An}{Bn},若lim(3An+Bn)=8,lim(6An-Bn)=1求lim(4An-Bn)与lim(AnBn)的值 lim(1+tan×)^1/x求极限求极限lim 2/(3^n-1) lim(1-x)^3/x 求极限~ 求lim(n-无穷)(sinn!/(n!+1)) lim (1+2/n)^n+4 n-->无穷大求极限求 lim(x→1)sin(x+1)/x+1 求 lim(x→2)x²-4/x-2 求lim(1-cosx)/x^2求lim(1-COSX)/X^2X→0 求lim(x->&无穷)sinn/n,求lim(x->无穷)sin(1/n) 极限的简单运算lim an=3, lim bn=1/3, 求lim ((an-3bn)/2an) 数学难题,求指教~~极限到底是什么玩意我还不懂.1.lim（x^2-2x+6）2.lim(x^2-4)/(x-2）3.lim(x^2-6x=8)/(x^-5x=4)4.lim[1/(1-x)-1/(1-x^3)5.lim(sin2x)/x^26.lim(sin5x)/x7.lim(tan3x)/(sin7x)8.lim[(1+x)/x]^2x例如这道例题~lim[(1/3)x+1] 已知LIM（3an+bn)=8,LIM(6an-bn)=1,求LIM（an*bn)令 lim（3An+Bn）=8 …… ①lim（6An-Bn）=1 …… ②①+② 得到 lim（9An）=9,解得lim（An）=1；①X2-② 得到 lim（3Bn）=15,解得lim（Bn）=5；这样解法错误,用待定系求lim(1-1/4)(1-1/9).(1-1/n^2) n趋于无穷 lim(1+2x)^1/x求极限（lim下是x~0) 若lim[(2n-1)an]=1 求lim(n*an)的值求极限lim(x→0)sinxsin(1/x);lim(x→∞)(arctanx/x)