\(\frac{1}{2}-\frac{1}{2016.2015}-\frac{1}{2015.2014}-...-\frac{1}{3.2}\)

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

\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}\right)\)

\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{2016}\right)\)

\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{2016}\)

\(=\frac{1}{2016}\)

\(\frac{1}{2}-\frac{1}{2016.2015}-\frac{1}{2015.2014}-...-\frac{1}{3.2}\)

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

\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2015}-\frac{1}{2016}\right)\)

\(=\frac{1}{2}-\left(\frac{1}{2}-\frac{1}{2016}\right)\)

\(=\frac{1}{2}-\frac{1}{2}+\frac{1}{2016}\)

\(=0+\frac{1}{2016}=\frac{1}{2016}\)

\(=\frac{2015-2014}{2015.2014}-\frac{2014-2013}{2014.2013}-\frac{2013-2012}{2013.2012}-...-\frac{2-1}{2.1}\)

\(=\left(\frac{2015}{2015.2014}-\frac{2014}{2015.2014}\right)-\left(\frac{2014}{2014.2013}-\frac{2013}{2014.2013}\right)-...-\left(\frac{2}{2.1}-\frac{1}{2.1}\right)\)

\(=\left(\frac{1}{2014}-\frac{1}{2015}\right)-\left(\frac{1}{2013}-\frac{1}{2014}\right)-\left(\frac{1}{2012}-\frac{1}{2013}\right)-...-\left(1-\frac{1}{2}\right)\)

\(=\frac{1}{2014}-\frac{1}{2015}-\frac{1}{2013}+\frac{1}{2014}-\frac{1}{2012}+\frac{1}{2013}-...-1+\frac{1}{2}\)

\(=\frac{1}{2014}-\frac{1}{2015}+\frac{1}{2014}-1=\frac{1}{1007}-\frac{1}{2015}-1=...\)

bai nay ban viet nguoc day so lai roi giai nhu binh thuong la duoc

b: \(=\dfrac{1}{2}-\left(\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2015}-\dfrac{1}{2016}\right)\)

\(=\dfrac{1}{2}-\dfrac{1}{2}+\dfrac{1}{2016}=\dfrac{1}{2016}\)

A=1/2015-1/2015.2014-....-1/3.2-1/2.1

A=1/2015-[1/2015.2014+1/2014.2013+....+1/3.2+1/2.1]

A=1/2015-[1/1.2+1/2.3+....1/2014.2015]

A=1/2015-[1-1/2+1/2-1/3+...+1/2014-1/2015]

A=1/2015-[1-2015]

A=1/2015-1+1/2015

A=[1/2015+1/2015]-1

A=2/2015-1

A=-2013/2015

5/4:1/4:(11/6-3/2)+1

5/4:1/4:1/3+1

5/4.4/1:1/3+1

5/4.4/1.3/1+1

5.1/3+1

5/3+1

5/3+1/1

5/3+3/3

8/3

\(125\%.\left(-\frac{1}{2}\right)^2:\left(1\frac{5}{6}-1,5\right)\)

\(=\frac{5}{4}.\left(-\frac{1}{2}\right)^2:\left(\frac{11}{6}-1,5\right)\)

\(=\frac{5}{4}.\frac{1}{4}:\left(\frac{11}{6}-\frac{3}{2}\right)\)

\(=\frac{5}{4}.\frac{1}{4}:\frac{1}{3}\)

\(=\frac{5}{4}:\frac{3}{4}=\frac{5}{3}\)

b, \(|\frac{2}{3}x-\frac{1}{2}|=\frac{5}{6}\)

\(\frac{2}{3}x-\frac{1}{2}=\frac{5}{6}\)hoặc\(-\frac{5}{6}\)

\(\frac{2}{3x}=\frac{5}{6}+\frac{1}{2}\)hoặc \(\frac{2}{3}x=-\frac{5}{6}+\frac{1}{2}\)

\(\frac{2}{3}x=\frac{4}{3}\)hoặc \(-\frac{1}{3}\)

\(x=\frac{4}{3}:\frac{2}{3}\)hoặc \(-\frac{1}{3}:\frac{2}{3}\)

\(x=2\)hoặc \(-\frac{1}{2}\)

Bài 2: 

\(=\frac{2017}{2016}\)

Bài 3 :

a, trên cùng một nửa mặt phẳng bờ chứa tia Ox, tia Oz nằm giữa 2 tia còn lại . Vì \(\widehat{xOz}< \widehat{xOy}\left(100< 50\right)\)

b, Vì tia Oz nằm giữa 2 tia còn lại nên ta có :

\(\widehat{yOz}+\widehat{zOx}=\widehat{xOy}\)

\(\widehat{yOz}+50=100\)

\(\widehat{yOz}=100-50=50\)

Vậy tia Oz là tia phân giác của góc \(\widehat{xOy}\).Vì tia Oz nằm giữa 2 tia còn lại và 2 góc yOz và zOx bằng nhau = 50

c, Vì tia Ot là tia đối của Ox nên có số đo là 180 nên \(\Rightarrow\)\(\widehat{xOt}=180\)

\(\left|\frac{2}{3}x-\frac{1}{2}\right|=\frac{5}{6}\)

\(\Rightarrow\frac{2}{3}x-\frac{1}{2}=\hept{\begin{cases}\frac{5}{6}\\-\frac{5}{6}\end{cases}}\)

\(\Rightarrow\frac{2}{3}x=\hept{\begin{cases}\frac{4}{3}\\-\frac{1}{3}\end{cases}}\)

\(\Rightarrow x=\hept{\begin{cases}2\\-\frac{1}{2}\end{cases}}\)

A= 1/1.2 + 1/2.3 +...........+ 1/2016.2015

  = 1 - 1/2 +1/2 - 1/3 + ............+1/2015 - 1/2016

  = 1 - 1/2016

  = 2015/2016

thank nhìu nha