Sửa đề: \(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\)
Ta có: \(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}\)
\(=\frac{1}{3}-\frac{1}{11}\)
\(=\frac{11}{33}-\frac{3}{33}=\frac{8}{33}\)
Tính hợp lý: \(B=\dfrac{2}{3.5}+\dfrac{2}{5.7}+\dfrac{2}{7.9}+...+\dfrac{2}{99.100}\)
Chứng tỏ rằng : B = 2/3.5+2/5.7+2/7.9+...+2/97.99
A = 2/3.5 + 2/5.7 + 2/7.9 + ... + 2/95.97 + 2/97.99
2/1.3+2/3.5+2/5.7+...+2/99.100
Tính Q =\(\dfrac{1.3}{3.5}+\dfrac{2.4}{5.7}+\dfrac{3.5}{7.9}+...+\dfrac{\left(n-1\right)\left(n+1\right)}{\left(2n-1\right)\left(2n+1\right)}+...+\dfrac{1002.1004}{2005.2007}\)
Cho \(P=\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{2019.2021}\)
chứng tỏ rằng P<1
1, 1/7 + 1/91 + 1/247 + 1/475 + 1/775 + 1/1147
2, 1/6 + 5/6.7 + 1/7.8 + 5/8.9 + ... + 1/24.25
3, 22/5.7 + 22/7.9 + 22/9.11 + ... + 22/39.41
a) 1/3-1/4
b) 1/4-1/5
c) S= 1/1.2+ 1/2.3+.........+1/N.(N+1)
d) M= 2/3.5+ 2/5.7+....+ 2/97.99
giải thích cho mik luôn ạ
Tính nhanh:
a, \(\dfrac{2}{1.3}+\dfrac{2}{3.5}+\dfrac{2}{5.7}+...+\dfrac{2}{201\times203}\)
b, \(\dfrac{-4}{2.5}-\dfrac{4}{5.8}-\dfrac{4}{8.11}-...-\dfrac{4}{2015.2018}\)
