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 编辑:作业帮 分类:综合作业 时间:2024/05/08 20:02:38
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.
由1/(2√1+1√2)+1/(3√2+2√3)+1/(4√3+3√4)+...+1/(100√99+99√100)
=(2√1-1√2)/(2√1+1√2)(2√1-1√2)+(3√2-2√3)/(3√2+2√3)(3√2-2√3)
+(4√3-3√4)/(4√3+3√4)(4√3-3√4)+...+(100√99-99√100)/(100√99+99√100)(100√99-99√100)
=(2-√2)/1×2+(3√2-2√3)/2×3+(4√3-3√4)/3×4+...+(100√99-99√100)/99×100
=(1-√2/2)+(√2/2-√3/3)+(√3/3-√4/4)+...+(√99/99-√100/100)
=1-√100/100
=1-1/10
=9/10.
=(2√1-1√2)/(2√1+1√2)(2√1-1√2)+(3√2-2√3)/(3√2+2√3)(3√2-2√3)
+(4√3-3√4)/(4√3+3√4)(4√3-3√4)+...+(100√99-99√100)/(100√99+99√100)(100√99-99√100)
=(2-√2)/1×2+(3√2-2√3)/2×3+(4√3-3√4)/3×4+...+(100√99-99√100)/99×100
=(1-√2/2)+(√2/2-√3/3)+(√3/3-√4/4)+...+(√99/99-√100/100)
=1-√100/100
=1-1/10
=9/10.
化简:|1-根号2|+|根号2-根号3|+|根号3-根号4|+.+|根号99-根号100|
|1-根号2|+|根号2-根号3|+|根号3-根号4|+...+|根号99-根号100|
根号1+根号2分之一+根号2+根号3分之一+...根号99+根号100
化简|1-根号2|+|根号2-根号3|+|根号3-根号4|+···+|根号99-根号100|
化简1/1+根号2 +1/根号2+根号3 +.+1/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/
化简:|1-根号2|+|根号2-根号3|+|根号3-根号4|+.+|根号2011-根号2012|
1/1+根号2+1/根号2+根号3+1/根号3+根号4+.+1/根号98+根号99=
(1+根号2+根号3)(1+根号2-根号3)
|根号6 - 根号2|+|根号2 - 1 | - |3-根号6|
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