\(E=\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+...+\frac{4}{97.99}\)
\(\Rightarrow E=2\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)\) (đặt 2 làm nhân tử chung để ta có các số hạng trong ngoặc có hiệu 2 số ở mẫu = tử)
\(\Rightarrow E=2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(\Rightarrow E=2.\left(1-\frac{1}{99}\right)\)
\(\Rightarrow E=2.\frac{98}{99}\)
\(\Rightarrow E=\frac{196}{99}\)
*Không biết có đúng ko :)
\(E=\frac{4}{1.3}+\frac{4}{3.5}+\frac{4}{5.7}+..+\frac{4}{97.99}\)
\(E=2.\left(\frac{2}{1.3}+\frac{2}{3.5}+..+\frac{2}{97.99}\right)\)
\(E=2.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+..+\frac{1}{97}-\frac{1}{99}\right)\)
\(E=2.\left(1-\frac{1}{99}\right)\)
\(E=2.\frac{98}{99}\)
\(E=\frac{196}{99}\)
\(E=\frac{4}{1\cdot3}+\frac{4}{3\cdot5}+...+\frac{4}{97\cdot99}\)
\(=\frac{2\cdot2}{1\cdot3}+\frac{2\cdot2}{3\cdot5}+...+\frac{2\cdot2}{97\cdot99}\)
\(=2\left(\frac{2}{1\cdot3}+...+\frac{2}{97\cdot99}\right)\)
\(=2\left(1-\frac{1}{3}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=2\left(1-\frac{1}{99}\right)\)
\(=2\left(\frac{99}{99}-\frac{1}{99}\right)=2\cdot\frac{98}{99}=\frac{196}{99}\)
#Hoq chắc _ Baccanngon
