已知数列{an}中a1=2,a(n+1)=(根号2-1)*(an+2),n∈1,2,3,...已知数列{an}中a1=2,a(n+1)=(根号2-1)*(an+2),n∈1,2,3,...(1)若数列{bn}中b1=2,b(n+1)=(3bn+4)/(2bn+3),n∈1,2,3,.,证明:根号2

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已知数列{an}中a1=2,a(n+1)=(根号2-1)*(an+2),n∈1,2,3,...已知数列{an}中a1=2,a(n+1)=(根号2-1)*(an+2),n∈1,2,3,...(1)若数列{bn}中b1=2,b(n+1)=(3bn+4)/(2bn+3),n∈1,2,3,.,证明:根号2
已知数列{an}中a1=2,a(n+1)=(根号2-1)*(an+2),n∈1,2,3,...
已知数列{an}中a1=2,a(n+1)=(根号2-1)*(an+2),n∈1,2,3,...
(1)若数列{bn}中b1=2,b(n+1)=(3bn+4)/(2bn+3),n∈1,2,3,.,证明:根号2

已知数列{an}中a1=2,a(n+1)=(根号2-1)*(an+2),n∈1,2,3,...已知数列{an}中a1=2,a(n+1)=(根号2-1)*(an+2),n∈1,2,3,...(1)若数列{bn}中b1=2,b(n+1)=(3bn+4)/(2bn+3),n∈1,2,3,.,证明:根号2
由题:
设a(n+1)+x=(根号2-1)*(an+x)
结合a1=2,a(n+1)= (根号2-1)*(an+2),n∈1,2,3,...
解得:x= -根号2
所以{an-根号2}是等比数列.
an=根号2 * (根号2-1)^n+根号2
令t=(根号2-1)^(4n-1)
a4n-3=根号2*t/(根号2-1)^2+根号2
a4n-3=根号2*t*(根号2-1)^2+根号2
用数学归纳法:
1.k=1时,显然成立
2.k=n,n>=2,设2

好难