设数列{xn},{yn}中,x1=2且x(n+1)=(3xn+1)/(xn+3),yn=(xn-1)/(xn+1)(n∈N*).
(1)求证:数列{yn}是等比数列 (2)求yn的极限 (3)求xn的极限
人气:408 ℃ 时间:2019-12-17 08:05:46
解答
(1)∵x1=2x(n+1)=(3xn+1)/(xn+3),可以求出X2=7/5并求出Y1=1/3,Y2=1/6∴Y2/Y1=1/2∵yn=(xn-1)/(xn+1)∴yn+1=(X(n+1)-1)/(X(n+1)+1)将 x(n+1)=(3xn+1)/(xn+3)带入上式 得yn+1=(xn-1)/(2xn+2)∴yn+1/yn=(...
推荐
- X1=a>0,Y1=b>0,Xn+1=(Xn+Yn)/2,Yn+1=(Xn*Yn)^1/2,求证数列Xn,Yn的极限相等.其中两个n+1均为下角标
- 数列{Xn}满足X1=3/2,Xn+1={3Xn(n为奇数) Xn+N(n为偶数)} Yn=X2n-1+N + 1/2,n€N* 求证:数列{Yn}是等比数列
- 已知数列{xn},{yn}满足x1=5,y1=-5,3x(n+1)+2y(n)=7,6x(n)+y(n+1)=13,证xn=3^n+2 ,yn=1-2*3^n
- 已知数列{xn}满足x1=4,xn=4-4/Xn-1(n≥2),记yn=1/xn-2
- X1=a>0,Y1=b>0,Xn+1=(Xn+Yn)/2,Yn+1=(Xn*Yn)^1/2,求证数列Xn,Yn收敛并求其极限.其中两个n+1均为下角标
- 如图,在等边△ABC中,P为BC上一点,D为AC上一点,且∠APD=60°,BP=1,CD=23,则△ABC的边长为( ) A.3 B.4 C.5 D.6
- 已知曲线x^2/a^2-y^2/b^2=1(a>0,b>0)的离心率e=2根号3/3,直线L过点(a,0),B(0,-b)两点,原点O到L的距离是
- 求翻译这篇文章加答案最好thomas edison was a famous american scietist
猜你喜欢