Ta có nhận xét: \(\frac{2}{k\left(k+1\right)\left(k+2\right)}=\frac{1}{k\left(k+1\right)}-\frac{1}{\left(k+1\right)\left(k+2\right)}\)

Áp dụng tính A ta có:

\(2.A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{2014.2015.2016}\)

\(\Rightarrow2.A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2015}-\frac{1}{2015.2016}\)

\(\Rightarrow2.A=\frac{1}{1.2}-\frac{1}{2015.2016}=\frac{2015.1008-1}{2015.2016}\)

\(\Rightarrow A=\left(\frac{2015.1008-1}{2015.2016}\right):2\)

A = 1 - 1/2 - 1/3 + 1/2 - 1/3 - 1/4 + ... + 1/2014 - 1/2015 - 1/2016

A = 1- 1/2016

A = 2015/2016

A > 1/4

A=4949/19800 và 1/4

4949/19800 < 1/4

Xong! t*** mik đê!!!

\(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)

\(A=\frac{1}{2}\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{2015.2016}\right)\)

\(A=0,2499998...<0,25\)

\(\Rightarrow A<\frac{1}{4}\)

bạn viết gì vậy? Mình ko thấy?

A = 1/1.2.3 + 1/2.3.4 + 1/3.4.5 + ... + 1/2014.2015.2016

=> A = 1/2.(2/1.2.3 + 2/2.3.4 + 2/3.4.5 + ... + 2/2014.2015.2016)

=> A = 1/2.(1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + 1/3.4 - 1/4.5 + ... + 1/2014.2015 - 1/2015.2016)

=> A = 1/2.(1/2 - 1/2015.2016)

=> A < 1/2.1/2 = 1/4 

Ta có: \(A=\frac{1}{1.2.3}+\frac{1}{2.3.4}+....+\frac{1}{2014.2015.2016}\)

\(\Rightarrow2A=\frac{2}{1.2.3}+\frac{2}{2.3.4}+....+\frac{2}{2014.2015.2016}\)

\(\Rightarrow2A=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+....+\frac{1}{2014.2015}-\frac{1}{2015.2016}\)

\(\Rightarrow2A=\frac{1}{1.2}-\frac{1}{2015.2016}\)

\(\Rightarrow A=\left(\frac{1}{2}-\frac{1}{2015.2016}\right):2\)

\(\Rightarrow A=\frac{1}{4}-\frac{1}{2015.2016.2}\)

\(\Rightarrow A< \frac{1}{4}\)

Ta có: 

A = \(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{2014.2015.2016}\)

2A = \(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{2014.2015.2016}\)

2A = \(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{2014.2015}-\frac{1}{2015.2016}\)

2A = \(\frac{1}{1.2}-\frac{1}{2015.2016}\)

=> 2A < \(\frac{1}{1.2}=\frac{1}{2}\)

=> A < \(\frac{1}{4}\)

Vậy A < \(\frac{1}{4}\)

2A = [1/1.2-1/2.3]+[1/2.3-1/3.4]+...+[1/2014.2015-1/2015.2016]

2A = 1/1.2-1/2.3+1/2.3-1/3.4+...+1/2014.2015-1/2015.2016

2A = 1/1-1/2015.2016

2A = 2015.2016-1/2015.2016

A = \(\frac{\left[2015.2016-1\right]:2}{2015.2016}=0.4999998769\)

ban ơi.Số́ hơi to thì phả̉i