计算1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50
计算1/1*2*3+1/2*3*4+1/3*4*5+.+1/48*49*50
1/1*2*3+1/2*3*4+1/3*4*5+......+1/48*49*50
=（1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+……+1/48*19-1/49*50）÷2
=（1/1*2-1/49*50）÷2
=（1/2-1/2450）÷2
=1/4-1/4900
=1224/4900
=306/1225
1/1×3+1/2×4+1/3×5+.+1/49×51
1/[n*(n+2)]=1/2*[1/n-1/(n+2)]
2*原式=1/1-1/3+1/2-1/4+1/3-1/5+...+1/49-1/51=1+1/2-1/50-1/51=1862/1275
原式=931/1275
1/2+1/3+1/4+1/5+.+1/50=?
1/2+1/3=2+3/2*3=5/6
1/2+1/3+1/4=11/3*4
所以1/2+1/3+1/4+1/5+...+1/50=49*50-1/49*50=244*/2450
1/2÷3+1/3÷4+1/4÷5+.+1/2010÷2011=
1/2÷3+1/3÷4+1/4÷5+......+1/2010÷2011
=1/2 x1/3+1/3 x1/4+1/4 x1/5+......1/2010 x1/2011
=1/2-1/3+1/3-1/4+1/4-1/5+......+1/2010-1/2011
=1/2-1/2011
=2011/4022-2/4022
=2009/4022
不懂继续问哦^_^
1/1*3+1/2*4+1/3*5+.+1/2005*2007
题目是1/(1*3)+1/(2*4)+...吗？
因为1/(1*3)=1/2*(1/1-1/3)
所以原式=1/2*(1/1-1/3)+1/2*(1/2-1/4)+1/2*(1/3-1/5)+1/2*(1/4-1/6)+...
=1/2*(1/1+1/2-1/2006-1/2007)
1/1*2+1/2*3+1/3*4+1/4*5+.+1/24*25
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/24-1/25)
=1-1/25
=24/25
1/1*2+1/2*3+1/3*4+1/4*5+.+1/1000*1001
1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)+……+1/(1000×10001)
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/1000-1/1001)
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+……+1/1000-1/1001
=1-1/1001
=1000/1001
希望对你有帮助
1/1*2+1/2*3+1/3*4+1/4*5+.+1/2005*2006
1/1*2+1/2*3+1/3*4+1/4*5+......+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*2+1/2*3+1/3*4+1/4*5+.+1/2004*2005=?
原式=1-1/2+1/2-1/3+……+1/2004-1/2005
=2004/2005
1/1*2+1/2*3+1/3*4+1/4*5+.+1/2001*2002=
1/1*2+1/2*3+1/3*4+1/4*5+...+1/2001*2002
=1-1/2+1/2-1/3+1/3-1/4+...+1/2001-1/2002
=1-1/2002
=2001/2002
