已知数列{an}中,a1=2,an+1=(根号2-1)(an+2),n=1,2,3,4.,求{an}通项公式“根号2-1”仅2带根号,an+1是整体an+1的n+1是角标,是第n+1项

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已知数列{an}中,a1=2,an+1=(根号2-1)(an+2),n=1,2,3,4.,求{an}通项公式“根号2-1”仅2带根号,an+1是整体an+1的n+1是角标,是第n+1项
已知数列{an}中,a1=2,an+1=(根号2-1)(an+2),n=1,2,3,4.,求{an}通项公式
“根号2-1”仅2带根号,an+1是整体
an+1的n+1是角标,是第n+1项

已知数列{an}中,a1=2,an+1=(根号2-1)(an+2),n=1,2,3,4.,求{an}通项公式“根号2-1”仅2带根号,an+1是整体an+1的n+1是角标,是第n+1项
an+1=(√2+1)an+2
an+1/an+2=√2+1
an/an+1=√2+1
an-1/an=√2+1
、、、
a1/a2=√2+1
将等式相乘最后有
a1/an=(√2+1)^(n-1)
所以
an=2/(√2+1)^(n-1)