whs7611
幼苗
共回答了15个问题采纳率:93.3% 举报
1.
A(n+1)-1=(4-4An)/((An)-3)
A(n+1)+1=(-2-2An)/((An)-3)
两式相除
B(n+1)=(A(n+1)-1)/(A(n+1)+1)=2((An)-1)/((An)+1)=2Bn
B1=((A1)-1)/((A1)+1)=(-3-1)/(-3+1)=2
{Bn}是以2为首项,2为公比的等比数列.
Bn=2^n
2.
Tn=5/2+7/4+9/8+……+(2n+3)/2^n
两边同乘公比2
2Tn=5+7/2+9/4+……+(2n+3)/2^(n-1)
两式错位相减
2Tn-Tn=5+[(7/2-5/2)+(9/4-7/4)+(11/8-9/8)+……+((2n+3)/2^(n-1)-(2n+1)/2^(n-1)]-(2n+3)/2^n
=5+[2/2+2/4+2/8+……+2/2^(n-1)]-(2n+3)/2^n
=5+1×(1-(1/2)^(n-1))/(1-1/2)-(2n+3)/2^n
=7-(2n+7)/2^n
Tn
1年前
2