求数列an=1/(16n^2+8n-3)的前n项和

问题描述:

求数列an=1/(16n^2+8n-3)的前n项和

∵an=1/(16n²+8n-3)=1/[(4n-1)(4n+3)]=[1/(4n-1)-1/(4n+3)]/4
∴Sn=1/4×﹛(1/3-1/7)+(1/7-1/11)+…+[1/(4n-1)-1/(4n+3)]﹜
=1/4×[1/3-1/(4n+3)]
=n/[3(4n+3)]