计算:1/[a(a+1)]+1/[(a+1)(a+2)]+1/[(a+2)(a+3)+...+1/[(a+2006)(a

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/17 20:00:02

计算:1/[a(a+1)]+1/[(a+1)(a+2)]+1/[(a+2)(a+3)+...+1/[(a+2006)(a+2007)]

1/[a(a+1)]=1/a-1/(a+1)
1/[(a+1)(a+2)]=1/(a+1)-1/(a+2)
1/[(a+2)(a+3)]=1/(a+2)-1/(a+3)
……
1/[(a+2005)(a+2006)]=1/(a+2005)-1/(a+2006)
1/[(a+2006)(a+2007)]=1/(a+2006)-1/(a+2007)
原式
1/[a(a+1)]+1/[(a+1)(a+2)]+1/[(a+2)(a+3)+...+1/[(a+2006)(a+2007)]
=1/a-1/(a+1)+1/(a+1)-1/(a+2)+1/(a+2)-1/(a+3)+……+1/(a+2005)-1/(a+2006)+1/(a+2006)-1/(a+2007)
=1/a-1/(a+2007)
=2007/[a(a+2007)]

(a+1)(a+2)(a-3)计算计算a^3/a-1-a^2-a-1 计算 a^2/1+a+1-a 计算(a+1)(a+2)(a+3)(a-6) (a 1)(a 2)(a 3)(a 计算：1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2006)(a+2007) 计算2a(a-3)^1-6a^2(3-a)-8a(a-3) 计算：a+1/a-1+a-2/1-a a(a-1)(a-2)(a-3)(a-4)因式分解计算1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008) 计算1/a(a+1)+1/(a+1)(a+2)+...+1/(a+2007)(a+2008)+1/(a+2011)(a+ 计算：1/(a(a+2))+1/((a+2)(a+4))+1/((a+4)(a+6))+...+1/((a+18)(a+