Question

等比数列与等差数列 等差数列an各项均为正,a1=3,前n项和为Sn,bn为等比数列,b1=1.b2×S2=64,b3×

Answer 1

1、设公差为d,公比为q.

2、数列表达式 an=3+(n-1)d ;;bn=q^(n-1) ;Sn=(a1+an)*n/2=3n+(n-1)nd/2

3、列方程①q(6+d)=64; ②q^2*（9+3d)=960 解得q=8 ;d=2或q=40/3 d=-6/5(不符题意舍去）

4、写出 an=3+2(n-1)=2n+1 bn=8^(n-1) ;sn=n^2+2n=n(n+2)=1/2*[1/n-1/(n+2)]

5、1/S1+1/S2+...+1/Sn=1/2*[1-1/3+1/2-1/4+1/3-1/5+...+1/n-1/(n+2)]

=1/2[1+1/2-1/(n+1)-1/(n+2)]=3/4-(n+3/2)/[(n+1)(n+2)]