\(\dfrac{6}{1.3}+\dfrac{6}{3.5}+...+\dfrac{6}{99.100}\\ =3\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{99.100}\right)\\ =3\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{99}-\dfrac{1}{100}\right)\\ =3\left(1-\dfrac{1}{100}\right)\\ =3.\dfrac{99}{100}\\ =\dfrac{297}{100}\)
\(T=\dfrac{4}{1.3}+\dfrac{4}{3.5}+\dfrac{4}{5.7}+....+\dfrac{4}{99.100}\)
Bài 5: Tính nhanh tổng sau(nếu có):
M=\(\dfrac{3}{2}\)-\(\dfrac{5}{6}\)+\(\dfrac{7}{12}\)-\(\dfrac{9}{20}\)+\(\dfrac{11}{30}\)-\(\dfrac{13}{42}\)+\(\dfrac{15}{56}\)-\(\dfrac{17}{72}\) ; A=\(\dfrac{5}{1.3}\)+\(\dfrac{5}{3.5}\)+\(\dfrac{5}{5.7}\)+.....+\(\dfrac{5}{2019.2021}\)
\(\dfrac{5}{1.3}\)+\(\dfrac{5}{3.5}\)+\(\dfrac{5}{5.7}\)+...+\(\dfrac{5}{201.203}\)
\(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + ... + \(\dfrac{2}{95.97}\)
\(\dfrac{7}{1.3}\) + \(\dfrac{7}{3.5}\) + \(\dfrac{7}{5.7}\) + ... + \(\dfrac{7}{2021.2023}\)
\(\dfrac{1}{1.3}\) +\(\dfrac{1}{3.5}\) +\(\dfrac{1}{5.7}\) +.....+\(\dfrac{1}{2003.2005}\)
\(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...\dfrac{2}{2021.2023}\)
\(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + \(\dfrac{2}{7.9}\) + ... + \(\dfrac{2}{2020.2022}\)
\(\dfrac{7}{1.3}\) + \(\dfrac{7}{3.5}\) + \(\dfrac{7}{5.7}\) + ... + \(\dfrac{7}{2021+2023}\)
