Question

x1=10,xn+1(注:n+1为下标)=根号下(6+xn),证明极限存在,并求该极限.

Answer 1

x1=10,xn+1(注:n+1为下标)=根号下(6+xn),

x2=√(6+10)=4,

x3=√(6+4)=√10,

x4=√(6+√10)

.

xn+1=√(6+xn)

下面证明数列xn是有界单调减数列对于n=1,2有x2