4×4/3×5+6×6/5×7······+18×18/17×19用列项做.过了今天就不

Question

4×4/3×5+6×6/5×7······+18×18/17×19 用列项做.过了今天就不

Answer 1

an=(2n+2)^2/[(2n+2)^2-1]=1+1/[(2n+2)^2-1]=1+[1/(2n+1)-1/(2n+3)]/2
sn=n+[1/3-1/(2n+3)]/2
当n=8 (2n+2=18)
sn=8+(1/3-1/19)/2=8又8/57