等差数列{an}的各项均为正数,a1=1,前n项和为sn,数列{bn}为等比数列,b1=1,且b2s2=6,b2+s3=8(1)秋数列{an}与{bn}的通项公式(2)求1/S1+1/S2+L+1/SN
问题描述:
等差数列{an}的各项均为正数,a1=1,前n项和为sn,数列{bn}为等比数列,b1=1,且b2s2=6,b2+s3=8(1)秋数列{an}与{bn}的通项公式(2)求1/S1+1/S2+L+1/SN
第二问是求1/S1+1/S2+……+1/SN
答
(1)假设等差数列{an}的公差为d,假设等比数列{bn}的公比为q则根据题意b2s2=6,b2+s3=8可得q(1+1+d)=6q+(1+1+d+1+d+d)=8整理q(2+d)=6.①q+3d=5.②由二式可得q=(5-3d)代入①式得(5-3d)(2+d)=6整理得3d²+d-4=0...