\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{9900}+x=100\)
\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{99.100}+x=100\)
\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{99}-\frac{1}{100}+x\right)=100\)
\(\left(1-\frac{1}{100}\right)+x=100\)
\(\frac{99}{100}+x=100\)
\(x=100-\frac{99}{100}=\frac{9901}{100}\)
\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+....+\frac{1}{99.100}+x=100\)
\(\Rightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{2}{3}+....+\frac{1}{99}-\frac{1}{100}+x=100\)
\(\Rightarrow1-\frac{1}{100}+x=100\)
\(\Rightarrow\frac{99}{100}+x=100\)
\(\Rightarrow x=100-\frac{99}{100}\)
\(\Rightarrow x=\frac{1}{100}\)
~Chúc bạn hok tốt~
1/1.2+1/2.3+1/3.4+1/4.5+...+1/99.100+x=100
1/1-1/2+1/3-1/4+1/4-1/5+...+1/99-1/100+x=100
1/1-1/100+x=100
99/100+x=100
x=100-99/100
x=9901/100
Chúc bạn tốt nha!
Ta có : 1/2 + 1/6 + 1/12 + 1/20 + ...... + 1/9900 + x = 100 .
=> 1/1.2 + 1/2.3 + 1/3.4 + 1/4.5 +...... + 1/99.100 + x = 100 .
=> 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ...... + 1/99 - 1/100 + x = 100 .
=> 1 - 1/100 + x = 100 .
=> 99/100 + x = 100 .
=> x = 100 - 99/100 .
=> x = 9901/100 .
Vậy x = 9901/100 .
