Question

求数学大神帮忙！！

Answer 1

an -1=1-1/an-1=(an-1 -1)/an-1;bn=1/(an -1)=an-1/(an-1 -1);

bn - bn-1=an-1/(an-1 -1) -an-2/(an-2 -1)=an-1*an-2/(an-2 -1)-an-2/(an-2 -1)=(an-1-1)an-2/(an-2 -1)=(an-1 -1)/(an-2 -1) *an-2=1/an-2 *an-2=1;即数列bn是等差数列b1=1/(a1-1)=-4/3;则
bn=-4/3+(n-1)*1=n-7/3.
an=1/(bn) +1=1/(n-7/3) +1=(3n-4)/(3n-7)=1+3/(3n-7)要使得最大值即3n-7＞0；但3n-7为分母，值随n增大而递减；故取n=3时数列最大值amax=1+3/2=5/2=2.5；同理n=2时数列最小值amin=-2

Answer 2