第2个回答 2010-07-29
A1=1,A2=A+1,A3=2A+1.......An=(N-1)A+1
所以SN=[(N-1)A+2]*N/2
S2N=[(2N-1)A+2]*2N/2
因为S2N=4SN
解得:-2A+4=-4A+8
所以A=2
故通式AN=(N-1)A+1=(N-1)*2+1=2N-1
Sn=(1+2n-1)n/2=n^2
bn=(2n-1)*2^(n-1)
Tn=1*2^0+3*2+5*2^2+...+(2n-1)*2^(n-1)
2Tn=1*2^1+3*2^2+5*2^3+...+(2n-1)*2^n
Tn-2Tn=1*2^0+2[2+2^2+...+2^(n-1)]-(2n-1)*2^n
-Tn=1+2*2(1-2^(n-1))/(1-2)-(2n-1)2^n=1-4(1-2^n/2-(2n-1)2^n=1-4+2*2^n-(2n-1)2^n=-3+(3-2n)2^n
故Tn=3-(3-2n)2^n