1/1 + 1/1+2 + 1/1+2+3 + 1/1+2+3+4 +...........+1/1+2+3+4+5+6+7+8+9+10=???
来源:百度知道 编辑:UC知道 时间:2024/09/20 20:44:40
据说是国际级奥林匹克的题 在线等答案
20/11
=1+3+6+...10(1+10)/2=220它的通项式是n(n+1)/2
1/(1+2+3+...+n)=1/(n(n+1)/2)=2/n(n+1)
=2(1/n-1/n+1)
1/1 + 1/1+2 + 1/1+2+3 + 1/1+2+3+4 +...........+1/1+2+3+4+5+6+7+8+9+10
=1+2(1/2-1/3)+2(1/3-1/4)+...+2(1/10-1/11)
=1+2(1/2-1/11)
=2-2/11
=20/11
原式=1+(1+2)+(1+2+3)+(1+2+3+4)+......+(1+2+3+4+...+9+10)=1*10+2*9
3*8+...+9*2+10*1=2*[(1*10+2*9+3*8+4*6)]+5*5=2*76+25=177
1/( )+1/( )+1/( )+1/( )+1/( )+1/( )=1
(1/2005-1)(1/2004-1)........(1/3-1)(1/2-1)
(1-1/100)(1-1/99)(1-1/98)......(1-1/3
(1-1/2)(1-1/3)(1-1/4)(1-1/5).....(1-1/1000)
(1/2003-1)(1/2002-1)(1/2001-1)...*(1/1001-1)(1/1000-1)
(1-1/4)(1-1/9)(1-1/16)^(1-1/4008004)(1-1/4012009)
1/8=1/( )+1/( )1 1/10=1/( )+1/( )1/12=1/( )+1/( )+1/( )
1+1/2+1+1/3+1+1/4+......+1/100=?
1+1/2+1/3+.....+1/n
1+1/2+1/3+...+1/100