“1/1+√2+1/√2√3+1/√3+√4+……+1/√98+√99+1/√99+√100”怎么化简?

来源：学生作业帮助网 编辑：作业帮 时间：2024/05/10 17:49:08
“1/1+√2+1/√2√3+1/√3+√4+……+1/√98+√99+1/√99+√100”怎么化简?

“1/1+√2+1/√2√3+1/√3+√4+……+1/√98+√99+1/√99+√100”怎么化简?
“1/1+√2+1/√2√3+1/√3+√4+……+1/√98+√99+1/√99+√100”怎么化简?

“1/1+√2+1/√2√3+1/√3+√4+……+1/√98+√99+1/√99+√100”怎么化简?
1/1+√2)+(1/√2+√3)+(1/√3+√4)+.+(1/√n+√n+1)
=(1/1+1/√2+1/√3+……+1/√n)+(√2+√3+√4+……+√n+1)
=(1/√n)!+(√n+1)!
=[1/√n(1/√n +1)÷2]+[√n+1(√n+1 +1)÷2]
=(1/n+1/√n+ n+1+√n+1)/2
用这个套

计算：√1/(√1+√2010)+√2/(√2+√2009)+√3/(√3+√2008)+...+√2010/(√2010+√1) 计算:√4-√3/√12+√3-√2/√6+√2-√1/√2=? |√6-√2|+|1-√2|+|√6-3| 1/√3+√2+1/√4+√3+1/√5+√4+1/√6√5 √18×√1/2-√3/√12= (√6-√60)*√3-√1/2=? 1/(1+√2)+1/(√2+√3)+1/(√3+√4)+.1/(√2012+√2013) 2/3√2-√1/2+√8-√3+√12-√18 2√2（√2+1/√2）-（√27-√12/√3） 1/(√2009+√2008)+1/(√2008+√2007)+.+1/(√3+√2)+1/(√2+1) 1 √32-3√1/2+√22 √12+√27/√3-√1/3×√123 √50+√30/√8-44 √24+√216/√6+55 （√6-2√15）×√3-6√1/26 √2/3-4√216+43√1/67 √8+√30-√28 √1/7+√63-√1129 √40-5√1/10+√1010 √2+√8/√2 1 √2 √3 √6 1 √2 √3 √6 1 √2 √(1-√2)^2+√(√2-√3)^2.+√(√99-√100)√(1-√2)^2+√(√2-√3)^2....+√(√99-√100)^2 化简1/1+√2+1/√2+√3+...+1/√8+√9 1/1+√2+1/√2+√3+…+1/√2013+√2014= |√6|-√2+√（√2-1）² -√（√6-3）² /√1-√2/+/√2-√3/+…+/√99-√100/ 用规律计算：1／1+√2+1／√2+√3+1／√3√4+、、、+1／√2008+√2009+1／√2009√2010+1／√2010+√2011根据(√2-1)*(√2+1)=1(√3-√2)*(√3+√2)=1(√2005-√2004)*(√2005+√2004)=1