星际战甲trinity prime:1-2/1*(1+2)-3/(1+2)(1+2+3)-4/(1+2+3)(1+2+3+4)...-100/(1+2+3...+99)(1+2+3...+100)

来源:百度文库 编辑:高校问答 时间:2024/03/29 17:17:58
初一的奥数题目

原式=1-2*(1/2-1/6+1/6-1/12+1/12-1/20+......+1/9900-1/10100
=1-2*(1/2-1/10100)
=1-10098/10100
=1/5050

1-2/1*(1+2)-3/(1+2)(1+2+3)-4/(1+2+3)(1+2+3+4)...-100/(1+2+3...+99)(1+2+3...+100)
=1-( 1/1-1/(1+2) )-( 1/(1+2)-1/(1+2+3) )...-( 1/(1+2+3+...+99) - 1/(1+2+3+...+100) )
=1-1/1+1/(1+2)-1/(1+2)+1/(1+2+3)-1/(1+2+3)...-1/(1+2+3+...+99)+ 1/(1+2+3+...+100)
=1/(1+2+3+...+100)
=1/5050

1-2/1*(1+2)-3/(1+2)(1+2+3)-4/(1+2+3)(1+2+3+4)...-100/(1+2+3...+99)(1+2+3...+100)
=1-( 1/1-1/(1+2) )-( 1/(1+2)-1/(1+2+3) )...-( 1/(1+2+3+...+99) - 1/(1+2+3+...+100) )
=1-1/1+1/(1+2)-1/(1+2)+1/(1+2+3)-1/(1+2+3)...-1/(1+2+3+...+99)+ 1/(1+2+3+...+100)
=1/(1+2+3+...+100)

1-2/1*(1+2)-3/(1+2)(1+2+3)-4/(1+2+3)(1+2+3+4)...-100/(1+2+3...+99)(1+2+3...+100)
=1-( 1/1-1/(1+2) )-( 1/(1+2)-1/(1+2+3) )...-( 1/(1+2+3+...+99) - 1/(1+2+3+...+100) )
=1-1/1+1/(1+2)-1/(1+2)+1/(1+2+3)-1/(1+2+3)...-1/(1+2+3+...+99)+ 1/(1+2+3+...+100)
=1/(1+2+3+...+100)