1/(2根号1+1根号2)+1/(3根号2+2根号3)+.+1/(100根号99+99根号100)

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/30 13:46:56

1/(2根号1+1根号2)+1/(3根号2+2根号3)+.+1/(100根号99+99根号100)
1/(2根号1+1根号2)+1/(3根号2+2根号3)+.+1/(100根号99+99根号100)

1/(2根号1+1根号2)+1/(3根号2+2根号3)+.+1/(100根号99+99根号100)
1/(2根号1+1根号2)
=(2根号1-1根号2)/(4-2)
=根号1-(根号2)/2
1/(3根号2+2根号3)
=(3根号2-2根号3)/(18-12)
=(根号2)/2-(根号3)/3
1/(2根号1+1根号2)+1/(3根号2+2根号3)+.+1/(100根号99+99根号100)
=根号1-(根号)/2+(根号)/2-(根号3)/3+(根号)/3-...+(根号99)/99-(根号100)/100
=根号1-(根号100)/100
=1-1/10
=9/10

1/(2+根号2)=(2-根号2)/(2+根号2)*(2-根号2)
=(2-根号2)/2
=1-(根号2)/2
1/(3根号2+2根号3)=(3根号2-2根号3)/(3根号2-2根号3)*(3根号2+2根号3) =(3根号2-2根号3)/6
=(根号2)/2 -(根号3)/3

全部展开

1/(2+根号2)=(2-根号2)/(2+根号2)*(2-根号2)
=(2-根号2)/2
=1-(根号2)/2
1/(3根号2+2根号3)=(3根号2-2根号3)/(3根号2-2根号3)*(3根号2+2根号3) =(3根号2-2根号3)/6
=(根号2)/2 -(根号3)/3
同理,1/(100根号99+99根号100)=(根号99)/99 -(根号100)/100
所以, 1/(2根号1+1根号2)+1/(3根号2+2根号3)+.......+1/(100根号99+99根号100)
=[1-(根号2)/2]+[(根号2)/2-(根号3)/3]+......+[(根号99)/99 -(根号100)/100]
=1-(根号100)/100
=1-1/10=0.9

收起

化简：|1-根号2|+|根号2-根号3|+|根号3-根号4|+.+|根号2011-根号2012| 化简：|1-根号2|+|根号2-根号3|+|根号3-根号4|+.+|根号99-根号100| 计算:/1-根号2/+/根号3-根号2/+/根号3-根号4/./根号2009-根号2010/ |1-根号2|+|根号2-根号3|+|根号3-根号4|+...+|根号99-根号100| 根号3+(-1)×(根号3-根号2) 根号3分之根号12×根号2-根号1/2 计算：根号18×根号1/2-根号12/根号3 1/根号3+根号2 计算|1-根号2|+|根号2-根号3|+|根号3-2|+|2-根号5|+.+|根号2008-根号2009|-根号2009 (根号3-根号2)分之1-根号2(根号3-根号2)分之(1-根号2) |1-根号2|-|根号3-根号2|+|根号2-根号3|+|根号8|RT. 根号1+根号2分之一+根号2+根号3分之一+...根号99+根号100 根号下(根号2+1)²+根号3(根号3-根号6)+根号8 计算 1*根号2*根号3*根号5*根号6*根号7*根号8咋算? |1-根号2|+|根号2-根号3|+|根号3-根号4|+|根号4-根号5|+.+|根号2012-根号2013|（结果保留根号） 根号1+根号2+根号3+根号4+根号5+根号6+根号7+根号8+根号9+根号10等于多少 化简 根号8+根号18 2根号12+根号48 3根号20-根号45-根号5分之1 根号9分之2+根号50-根号32化简 根号8+根号182根号12+根号483根号20-根号45-根号5分之1根号9分之2+根号50-根号326-根号2分之3-根号3分之2 根号1+根号2+.+根号9=?