1/1*2+1/2*3+1/3*4+……+1/2004*2005+1/2005*2006 1/1*3+1/3*5+1/5*7+……+1/49*51

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/02 18:21:03
1/1*2+1/2*3+1/3*4+……+1/2004*2005+1/2005*2006 1/1*3+1/3*5+1/5*7+……+1/49*51

1/1*2+1/2*3+1/3*4+……+1/2004*2005+1/2005*2006 1/1*3+1/3*5+1/5*7+……+1/49*51
1/1*2+1/2*3+1/3*4+……+1/2004*2005+1/2005*2006 1/1*3+1/3*5+1/5*7+……+1/49*51

1/1*2+1/2*3+1/3*4+……+1/2004*2005+1/2005*2006 1/1*3+1/3*5+1/5*7+……+1/49*51
1/1*2+1/2*3+1/3*4+……+1/2004*2005+1/2005*2006
=1-1/2+1/2-1/3+1/3-1/4+……+1/2005-1/2006
=1-1/2006
=2005/2006
1/1*3+1/3*5+1/5*7+……+1/49*51
=1/2*(2/1*3+2/3*5+2/5*7+……+2/49*51)
=1/2*(1-1/3+1/3-1/5-1/5-1/7+……+1/49-1/51)
=1/2*(1-1/51)
=25/51

(1)原式=1-1/2+1/2-1/3+1/3-1/4+……-1/2005+1/2005-1/2006=1-1/2006=2005/2006
(2)原式=1/2(1-1/3+1/3-1/5+1/5-……-1/49+1/49-1/51)=1/2(1-1/51)=25/51

1、可以分成1-1/2+1/2-1/3+.....+1/2004-1/2005+1/2005-1/2006=1-1/2006=2005/2006

1/1*2+1/2*3+1/3*4+......+1/2004*2005+1/2005*2006
=1-1/2+1/2-1/3+.....+1/2005-1/2006=1-1/2006
=2005/2006

1/1*3+1/3*5+1/5*7+……+1/49*51
=1/2(1-1/3)+1/2(1/3-1/5)+1/2(1/5-1/7)+......+1/2(1/49-1/51)
=1/2(1-1/3+1/3-1/5+1/5-1/7+........+1/49-1/51)
=1/2(1-1/51)
=1/2*50/51
=25/51

数字打出来不方便。

1+2+3+4+……+10000 1×2×3×4……×101 1+2+3+4……+101 1+2+3+4+5…………+100000000 (1/2+1/3+1/4+……+1/2013)(1+1/2+1/3+1/4+……+1/2012）-（1+1/2+1/3+……+1/2013）（1/2+……+1/2012） （1/1+2）+（1/1+2+3）+（1/1+2+3+4）+………+（1/1+2+3+………+100） 1+2/2*1+2+3/2+3*1+2+3+4/2+3+4*……*1+2……+2001/2+3+……+2001= 1+2+3+4+5+6……………………+100000000=? 1/(1-1/2)/(1-1/3)/(1-1/4)/……/(1-1/2012) 2(3+1)(3^2+1)(3^4+1)……（3^32+1)+1 1+2+3+4……+100000好的加分…………急…………………………快…………………………………… (1/2+1/3+1/4+1/5+……+1/2007)*(1+1/2+1/3+1/4+……+1/2006)………………计算：(1/2+1/3+1/4+1/5+……+1/2007)*(1+1/2+1/3+1/4+……+1/2006)-（1+1/2+1/3+1/4+……+1/2007）*(1/2+1/3+1/4+^+1/2006)要求简算 求证：1/2^3 +1/3^3 +1/4^3 +……+1/(n+1)^3 求证：1/2^3 +1/3^3 +1/4^3 +……+1/(n+1)^3 1+1×2+1×2×3+1×2×3×4……1×2×……×n=? 求和:1/1×2+1/2×3+1/3×4+……+1/n(n+1) (1-1/2)×(1-1/3)×(1-1/4)……×（1-1/2008）计算方法 200×(1-1/2)×(1-1/3)×(1-1/4)×……×(1-1/100)=?