设数列{ Xn } 满足│Xn+1-Xn│≤k│Xn-Xn-1│,n=2,3,...(0

设数列{ Xn } 满足│Xn+1-Xn│≤k│Xn-Xn-1│,n=2,3,...(0 设数列{xn}满足xn+1=xn/2+1/xn,X0>0,n=0,1,2,3,...证明数列{xn}极限存在并求出其极限 已知数列｛Xn｝满足x1=1/2,xn+1=1/(1+xn),n∈N+,证明:|xn+1-xn|≤1/6*（2/5）^n 设X1>0,xn+1=3(1+xn) / 3+xn (n=1,2…)求lim xn. 已知数列{xn}满足x1=3,x2=x1/2,...,xn=1/2(xn-1+xn-2),n=3,4,...,则xn等于 设a>0,{Xn}满足X0>0,Xn+1=1/2(Xn+a/Xn) ,n+1是下标,n=0,1,2...,证明：{Xn} 已知数列xn满足xn-xn^2=sin(xn-1/n),证明xn的趋向正无穷的极限为0 已知x1≠1,x1>0,xn+1=xn(xn^2+3)/(3xn^2+1)(n∈N),求证：数列{xn}或者对任意正整数 已知数列{Xn}满足Xn+1=Xn^2+Xn,X1=a(a-1),数列{Yn}满足Yn=1/(Xn+1),设Pn=X/( 数列｛Xn｝中,X1>0,a>0,Xn+1=1/2(Xn+a/Xn). 设x0=1,x(n+1)=(xn+2)/(xn+1)(n>=0),证明数列{xn}收敛. 已知数列xn满足x1=4,x(n+1)=（xn^2-3）/(2xn-4）