求数列1/(1×5),1/(5×9) ,…,1/(4n-3)(4n+1)的前n项和
问题描述:
求数列1/(1×5),1/(5×9) ,…,1/(4n-3)(4n+1)的前n项和
答
sn=1/(1*5)+ 1/(5*9)+.+1/(4n-3)(4n+1)=1/4*(1-1/5)+1/4*(1/5-1/9)+.+1/4*[1/(4n-3)-1/(4n+1)]=1/4*[1-1/5+1/5-1/9+.+1/(4n-3)-1/(4n+1)]=1/4*[1-1/(4n+1)]=1/4*4n/(4n+1)=n/(4n+1)