\(\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{97.99}\right)-x=-\frac{100}{99}\)
\(\Rightarrow\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{97}-\frac{1}{99}\right)-x=-\frac{100}{99}\)
\(\Rightarrow\left(1-\frac{1}{99}\right)-x=-\frac{100}{99}\)
\(\Rightarrow\frac{98}{99}-x=-\frac{100}{99}\)
\(\Rightarrow x=\frac{98}{99}-\left(-\frac{100}{99}\right)\)
\(\Rightarrow x=\frac{198}{99}=2\)
Vậy x = 2
tách\(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+\(\frac{2}{5.7}\)+......+\(\frac{2}{97.99}\)ra thành A
A=1/1-1/3+1/3-1/5+1/5-........+1/97-1/99
A=1-1/99=98/99
=>x=98/99-\(\frac{-100}{99}\)=2
k mình nha
\(\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)-x=-\frac{100}{99}\)
\(\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)-x=-\frac{100}{99}\)
\(\left(1-\frac{1}{99}\right)-x=-\frac{100}{99}\)
\(\frac{98}{99}-x=-\frac{100}{99}\)
\(\Rightarrow x=\frac{98}{99}-\left(-\frac{100}{99}\right)\)
\(\Rightarrow x=2\)
\(\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)-x=-\frac{100}{99}\)
\(\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}+...+\frac{1}{97}-\frac{1}{99}\right)-x=-\frac{100}{99}\)
\(\left(1-\frac{1}{99}\right)-x=-\frac{100}{99}\)
\(\left(\frac{99}{99}-\frac{1}{99}\right)-x=-\frac{100}{99}\)
\(\frac{98}{99}-x=-\frac{100}{99}\)
\(x=\frac{98}{99}-\left(-\frac{100}{99}\right)\)
\(\Rightarrow x=2\)
