Question

(3/4)*(8/9)*(15/16)*(24/25)*.它的极限是多少?

Answer 1

(3/4)*(8/9)=2/3=1/2+1/6 (3/4)*(8/9)*(15/16)=5/8=1/2+1/8 (3/4)*(8/9)*(15/16)*(24/25)=3/5=1/2+1/10 (3/4)*(8/9)*(15/16)*(24/25)*(35/36)=7/12=1/2+1/12 (3/4)*(8/9)*(15/16)*(24/25)*.*[(n+1)-1]/(n+1)=1/2+1/(2n+2) 1/(2n+2)的极限是0 1/2+1/(2n+2)的极限是1/2 (3/4)*(8/9)*(15/16)*(24/25)*.它的极限是1/2