(1^2+2^2)/12+(2^2+3^2)/23+...+(2000^2+2001^2)/20002001+(2001^2+2002^2)/20012002

来源：百度知道编辑：UC知道时间：2024/05/22 05:19:23

(1^2+2^2)/1*2+(2^2+3^2)/2*3+...+(2000^2+2001^2)/2000*2001+(2001^2+2002^2)/2001*2002
=(2-1)^2+2*1*2/1*2+(3-2)^2+2*3*2/2*3+...+(2001-2000)^2+2*2001*2000/2001*2000+(2002-2001)^2+2*2001*2002/2001*2002
=1/1*2+1/2*3+...+1/2000*2001+1/2001*2002+2*2001;
=(1-1/2+1/2-1/3_..+1/2000-1/2001+1/2001-1/2002)+4002;
=1-1/2002+4002=4002+2001/2002

你用现在的计算机按更方便啊

1/2-1/2=? (1+1/2)(1+1/2^2)(1+1/2^4)(1+1/2^8) (1-1/2^2)*(1-1/3^2)*(1-1/4^2).......(1-1/100^2) 3/2=2+1/1*2=1/1+1/2 1/1^2+1/2^2+...+1/n^2<2 1+1/(1+2)+1/(1+2+3)+...+1/(1+2+3+...+100) 1+1/(1+2)+1/(1+2+3)+-------+1/(1+2+3+----+100) 1+1/1+2+1/1+2+3+...+1/1+2+3...+2000 1+1/1+2+1/1+2+3.........+1/1+2+3.....100 1*(1/1+2)*(1/1+2+3)*~~~*(1/1+2+~~~2005)=?