设y1=10.yn+1=根号下6+yn n=1.2.试证明数列yn存在极限

大一数学数列极限：Y1=10,Yn+1 = (6+Yn)^(1/2),证明极限存在并求极限值. 大一高数问题:已知数列Yn有极限,且满足Yn+1(小1小n)=根号下2+Yn,则Yn的极限为? 数列极限证明lim(n=无穷大）Yn=1,Yn=(n^2+a^2)1/2*n 设数列{xn}有界,又limn->无穷yn=0,证明证明limXn．Yn=0,并由此结论求极限limn->无穷[n/(n 证明：若lim(n→∞)yn（数列yn）=A且A>0,则存在正整数N,当n>N时恒有yn>0. 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 设Yn=X(n-1)+2Xn,n=1,2,...证明:当数列Yn收敛时,数列Xn也收敛. yn=1/2(yn-1+2/yn-1)的极限 设yn=0.33.33 n个则当n趋向于无穷时,数列yn= 数列xn单调递增,yn单调递减,lim（xn-yn）=2（n趋向于正无穷）,证明Xn Yn 皆收敛. 设数列{xn}有界,有lim（yn）=0,证明：lim[（xn）×（yn）]=0 设Xn≤a≤Yn,lim(n→∞)《Yn-Xn》=0,则Xn与Yn