设Sn是等差数列{An}的前项和,若S3/S6=1/3,则S6/S12等于多少?要能看得懂的过程.
參考答案:设An＝A+nB
Sn=A1+A2+……+An
=(A+B)+(A+2B)+……+( A+nB)
=nA+(B+2B……+nB)
=nA+n(n+1)B/2
S3=3A+3×(3+1)/2×B＝3A+6B
S6=6A+6×(6+1)/2×B＝6A+21B
S12=12A+12×(12+1)/2×B＝12A+78B
S3/S6=1/3
(3A+6B)/(6A+21B)=1/3
A=B
S6/S12=(6A+21B)/( 12A+78B)=27A/90A=0.3
