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22 tháng 6 2019

\(C=\frac{1}{2}+\frac{1}{6}+...+\frac{1}{9900}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)

\(C=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{1}-\frac{1}{100}\)

\(=\frac{100}{100}-\frac{1}{100}\)

\(=\frac{99}{100}\)

7 tháng 5 2018

\(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}\)

\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(B=1-\frac{1}{100}\)

\(B=\frac{99}{100}\)

7 tháng 5 2018

\(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}\) 

  \(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

  \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

  \(=1+\left(-\frac{1}{2}+\frac{1}{2}\right)+\left(-\frac{1}{3}+\frac{1}{3}\right)+\left(-\frac{1}{4}+\frac{1}{4}\right)+...+\left(-\frac{1}{99}+\frac{1}{99}\right)-\frac{1}{100}\)

    \(=1-\frac{1}{100}=\frac{99}{100}\)

14 tháng 3 2020

_ giải bừa :v _

\(T=\frac{1}{2^2}+\frac{1}{4^2}+...+\frac{1}{14^2}\)

Ta thấy : \(\frac{1}{4^2}< \frac{1}{2.4};\frac{1}{14^2}< \frac{1}{12.14}\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{4^2}+...+\frac{1}{14^2}< \frac{1}{2^2}+\frac{1}{2.4}+...+\frac{1}{12.14}\)

\(\Rightarrow T< \frac{1}{2^2}+\frac{1}{2}\left(\frac{2}{2.4}+...+\frac{2}{12.14}\right)\)

\(\Rightarrow T< \frac{1}{2^2}+\frac{1}{2}.\left(\frac{1}{2}-\frac{1}{14}\right)\)

\(\Rightarrow T< \frac{1}{4}+\frac{1}{2}.\frac{3}{7}\)

\(\Rightarrow T< \frac{13}{28}\)

Mà \(\frac{13}{28}< \frac{1}{2}\Rightarrow T< \frac{1}{2}\)

....

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{9900}\)

\(A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\)

\(A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(A=1-\frac{1}{100}=\frac{100}{100}-\frac{1}{100}=\frac{99}{100}\)

\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+...+\frac{1}{9900}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}=\frac{99}{100}\)

31 tháng 5 2018

\(\frac{1}{2}+\frac{1}{6}\)\(+\frac{1}{12}\)\(+...+\frac{1}{9702}\)\(+\frac{1}{9900}\)

\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}\)\(+...+\frac{1}{98\cdot99}\)\(\frac{1}{99\cdot100}\)

\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\)\(\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(\frac{1}{1}-\frac{1}{100}\)

\(\frac{100}{100}\)\(\frac{1}{100}\)

\(\frac{99}{100}\)

31 tháng 5 2018

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9702}+\frac{1}{9900}\)

\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{98.99}+\frac{1}{99.100}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\)

\(=1-\frac{1}{100}\)

\(=\frac{99}{100}\)

22 tháng 6 2018

\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}+x=100\)

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}+x=100\)

\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}+x\right)=100\)

\(\left(1-\frac{1}{100}\right)+x=100\)

\(\frac{99}{100}+x=100\)

\(x=100-\frac{99}{100}=\frac{9901}{100}\)

22 tháng 6 2018

\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}+x=100\)

\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{2}{3}+....+\frac{1}{99}-\frac{1}{100}+x=100\)

\(\Rightarrow1-\frac{1}{100}+x=100\)

\(\Rightarrow\frac{99}{100}+x=100\)

\(\Rightarrow x=100-\frac{99}{100}\)

\(\Rightarrow x=\frac{1}{100}\)

~Chúc bạn hok tốt~

10 tháng 4 2018

\(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\)

\(\Rightarrow B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

         \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{99}-\frac{1}{100}\)

           \(=1-\frac{1}{100}\)

            \(=\frac{99}{100}\)

21 tháng 5 2019

\(B=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}\)

\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}\)

\(B=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}\)

\(B=1-\left(\frac{1}{2}-\frac{1}{2}\right)+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+...+\left(\frac{1}{99}-\frac{1}{99}\right)-\frac{1}{100}\)

\(B=1-\frac{1}{100}=\frac{99}{100}\)

~ Hok tốt ~

25 tháng 5 2016

A=1+2+3+4+5+...+99+100

A=(1+100).100:2=101.50=5050

B=1/2+1/6+1/12+1/20+1/30+...+1/9900

B=1/1.2+1/2.3+1/3.4+1/4.5+1/5.6+....+1/99.100

B=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/99-1/100

B=1-1/100=99/100

25 tháng 5 2016

A = 100 x 101 : 2 = 5050

\(B=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.........+\frac{1}{99.100}\)

    \(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{99}-\frac{1}{100}\)

      \(=1-\frac{1}{100}\)

        \(=\frac{99}{100}\)

14 tháng 4 2019

\(P=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\)

\(\Rightarrow P=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(\Rightarrow P=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow P=1-\frac{1}{100}\)

\(\Rightarrow P=\frac{99}{100}\)

14 tháng 4 2019

\(P=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{9900}\)

\(P=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{99.100}\)

\(P=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{99}-\frac{1}{100}\)

\(P=1-\frac{1}{100}\)

\(P=\frac{99}{100}\)

~Học tốt~

10 tháng 3 2016

lấy 1 - 1/9900= 9899/9900 chi có thế thôi

10 tháng 3 2016

9899/9900 thui