化简:1/(2+√2)+1/(3√2+2√3)+1/(4√3+3√4)+…+1/(100√99+99√100)化简:1/(2+√2)+1/(3√2+2√3)+1/(4√3+3*√4)+…+1/(100*√99+99*√100),√代表根号.
来源:学生作业学帮网 编辑:学帮网 时间:2024/06/01 11:15:51
化简:1/(2+√2)+1/(3√2+2√3)+1/(4√3+3√4)+…+1/(100√99+99√100)
化简:1/(2+√2)+1/(3√2+2√3)+1/(4√3+3*√4)+…+1/(100*√99+99*√100),√代表根号.
11
1/(2+√2)+1/(3√2+2√3)+1/(4√3+3√4)+…+1/(100√99+99√100)
=(2-√2)/(2^2-(√2)^2)+(3√2-2√3)/((3√2)^2-(2√3)^2)…+(100√99-99√100)/((100√99)^2-(99√100)^2)
=(2-√2)/(2*1)+(3√2-2√3)/(3*2)…+(100√99-99√100)/(100*99)
=1-1/√2+1/√2-1/1/√3…+1/√99-1/√100
=1-1/√100
1
其实就是1/[(n+1)√n+n√(n+1)]=[(n+1)√n-n√(n+1)]/[(n+1)√n+n√(n+1)]*
[(n+1)√n-n√(n+1)]=[(n+1)√n-n√(n+1)]/n(n+1)=1/√n-1/√(n+1)题目n=99
于是答案为1-1/√100
1/2+1/3+1/4+......+1/(2007x2008)=
22
楼上的说的队
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