首项为3公差为2的等差数列,(1/S1)+(1/S2)+.+(1/Sn)=?
问题描述:
首项为3公差为2的等差数列,(1/S1)+(1/S2)+.+(1/Sn)=?
答
Sk=(a1+ak)*k/2=[2a1+(k-1)d]*k/2=(2+k)k1/Sk=[(1/k)-1/(2+k)]/2所以S=1/S1+1/S2+...+1/Sn=(1/2)[(1-1/3)+(1/2-1/4)+(1/3-1/5)+……+(1/n)-1/(2+n)]=(1/2)[1+1/2-1/(n+1)-1/(n+2)]=3/4-[(2n+3)/2(n+1)(n+2)]