1/2+1/(2+4)+1/(2+4+6)+……+1/(2+4+6+...+20)=
(1-1/2^2)*(1-1/3^2)*...*(1-1/99^2)=
(1+1/1*3)*(1+1/2*4)*1(1+1/3*5)*...*(1+1/2001*2008)=
2*3/1*4+5*6/4*7+8*9/7*10+...+98*99/97*100=
(1^2+2^2)/1*2+(2^2+3^2)/2*3+...+(18^2+19^2)/18*19+(19^2+20^2)/19*20=
(2^2+1)/(2^2-1)+(4^2+1)/(4^2-1)+...+(18^2+1)/(18^2-1)+(20^2+1)/(20^2-1)=
求答案 谢谢
厉害,不过还有两道呢!还有两道呢! 帮下忙好吧 谢谢啦
追答你看得懂?怕你不懂,我都不想写了。(裂项法
(5)(1²+2²)/1×2+(2²+3²)/2×3+(3²+4²)/3×4+。。。+(19²+20²)/19×20
=(1/2+2/1)+(2/3+3/2)+(3/4+4/3)+(4/5+5/4)+。。。+(19/20+20/19)
=(2/1)+(1/2+3/2)+(2/3+4/3)+(3/4+5/4)+。。。+(19/20)
=2+2+2+。。。+2+19/20
=38又19/20.
(6)(2²+1)/(2²-1)+(4²+1)/(4²-1)+..+(18²+1)/(18²-1)+(20²+1)/(20²-1)
=1+2/(2²-1)+1+2/(4²-1)+。。。+1+2/(18²-1)+1+2/(20²-1)
=10+2/1×3+2/3×5+2/5×7+。。。+2/17×19+2/19×21
=10+[(1-1/3)+(1/3-1/5)+(1/5-1/7)+。。。+(1/17-1/19)+(1/19-1/21)]
=10+1-1/21
=10又20/21.