20减{（2的平方减一）分之（2的平方加一）加.加（20的平方减一）分之（20的平方加一}等于?

20-[(2^2+1)/(2^2-1)+(3^2+1)/(3^2-1)+.+(20^2+1)/(20^2-1)]
=20-[(2^2-1+2)/(2^2-1)+(3^2-1+2)/(3^2-1)+.+(20^2-1+2)/(20^2-1)]
=20-[(2^2-1)/(2^2-1)+2/(2^2-1)+(3^2-1)/(3^2-1)+2/(3^2-1)+.+(20^2-1)/(20^2-1)+2/(20^2-1)]
=20-[1+2/(2^2-1)+1+2/(3^2-1)+.+1+2/(20^2-1)]
=20-[20+2/(2^2-1)+2/(3^2-1)+.+2/(20^2-1)]
=20-[20+2/(2-1)(2+1)+2/(3-1)(3+1)+.+2/(20-1)(20+1)]
=20-[20+2/1*3+2/2*4+.+2/19*21]
=20-[20+1-1/3+1/2-1/4+.+1/19-1/21]
=20-[20+1-1/3+1/3-1/5+.+1/19-1/21+1/2-1/4+1/4-1/6+.+1/18-1/20]
=20-[20+1-1/21+1/2-1/20]
=20-[20+20/21+9/20]
=20-[20+200/420+189/420]
=20-[20+389/420]
=20-20-389/420
=-389/420