`= -2/3 . (2/(2.4) + 2/(4.6) + ... + 2/(98.100))`
`= -2/3 . (1/2 - 1/4 + 1/4 - 1/6 + ... + 1/98 - 1/100)`
`= -2/3 . 49/100`
`= -98/300 = -49/150`
\(\dfrac{1}{2.4}+\dfrac{1}{4.6}+\dfrac{1}{6.8}+...+\dfrac{1}{96.98}+\dfrac{1}{98.100}\)
\(l,\dfrac{\dfrac{3}{41}-\dfrac{12}{47}+\dfrac{27}{53}}{\dfrac{4}{41}-\dfrac{16}{47}+\dfrac{36}{53}}\)
\(m,\left(3-2\dfrac{1}{3}+\dfrac{1}{4}\right):\left(4-5\dfrac{1}{6}+2\dfrac{1}{4}\right)\)
\(n,F=\dfrac{4}{2.4}+\dfrac{4}{4.6}+\dfrac{4}{6.8}+...+\dfrac{4}{2008.2010}\)
\(p,F=\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{108}+...+\dfrac{1}{990}\)
B=\(\dfrac{1}{2.4}\)+\(\dfrac{1}{4.6}\)+\(\dfrac{1}{6.8}\)+\(\dfrac{1}{8.10}\)
Cho A= \(\dfrac{4}{2.4}\)+\(\dfrac{4}{4.6}\)+\(\dfrac{4}{6.8}\)+...+\(\dfrac{4}{46.48}\)+\(\dfrac{4}{48.50}\)
\(\dfrac{2^2}{1.3}\)x\(\dfrac{3^2}{2.4}\)x\(\dfrac{4^2}{3.5}\)......\(\dfrac{99^2}{98.100}\)
Chứng tỏ :
a, A = \(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{2022.2024}\) < \(\dfrac{1}{4}\)
b, B =\(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{2013.2015}< \dfrac{1}{2}\)
c, C =\(\dfrac{1}{3^2}+\dfrac{1}{5^2}+\dfrac{1}{7^2}+...+\dfrac{1}{2013^2}< \dfrac{1}{4}\)
d, D =\(\dfrac{1}{2^2}+\dfrac{1}{4^2}+\dfrac{1}{6^2}+...+\dfrac{1}{2014^2}< \dfrac{1}{2}\)
Tính
a,B=2.4+4.6+6.8+...+98.100
b,B=3+3.6+6.9+...+96.99
2/2.4+2/4.6+2/6.8+...+2/98.100
Tìm x, biết:
\(\dfrac{1}{2.4}+\dfrac{1}{4.6}+...+\dfrac{1}{\left(2x-2\right).2x}=\dfrac{11}{48}\) (x ϵ N , x ≥ 2)
\(2.4+4.6+6.8+....+98.100\)
