1/1*3+1/3*5+1/5*7+.1/2005*2007=?
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/17 16:11:08
1/1*3+1/3*5+1/5*7+.1/2005*2007=?
![1/1*3+1/3*5+1/5*7+.1/2005*2007=?](/uploads/image/z/17079823-55-3.jpg?t=1%2F1%2A3%2B1%2F3%2A5%2B1%2F5%2A7%2B.1%2F2005%2A2007%3D%3F)
1/1*3+1/3*5+1/5*7+...1/2005*2007
=(2/1*3+2/3*5+2/5*7+...+2/2005*2007)/2
因2/n*(n+2)=(n+2-n)/n(n+2)=1/n-1/(n+2)
所以
1/1*3+1/3*5+1/5*7+...1/2005*2007
=(1/1-1/3+1/3-1/5+...+1/2005-1/2007)/2
=1003/2007
=(2/1*3+2/3*5+2/5*7+...+2/2005*2007)/2
因2/n*(n+2)=(n+2-n)/n(n+2)=1/n-1/(n+2)
所以
1/1*3+1/3*5+1/5*7+...1/2005*2007
=(1/1-1/3+1/3-1/5+...+1/2005-1/2007)/2
=1003/2007
1/1*3+1/3*5+1/5*7+……1/2005*2007=?
(+1)+(-3)+(+5)+(-7)+...+(2005)+(-2007)
(+1)+(-3)+(+5)+(-7)+…+(2005)+(-2007)
计算:1/(1*3*5)+1/(3*5*7)+1/(5*7*9)+...+1/(2003*2005*2007)=?
1+3+5+7+...+2003+2005+2007+2009+2011=?
(-1)+3+(-5)+7+(-9)+...+(-2005)+2007+(-2009)=?
1+3+5+7+9+...+2003+2005+2007=?
1*3/1+3*5/1+5*7/1+...+2005*2007/1
1/1*3-1/3*5-1/5*7-.-1/2005*2007
计算:1/1×3+1/3×5+1/5×7+……+1/2005×2007+1/2007×2009
1+3+5+7+9+11.+2005+2007+2009
1+ 3+ 5 +7+ 9 +.+2003+2005+2007+2009+2011