VẾ TRÁI LÀ:

A=1/2.3+1/3.2+1/4.5+...+1/x[x+1]

A=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/n-1/n+1

A=1-1/n+1

1-1/n+1=2015/2016

1/n+1=1-2015/2016

1/n+1=1/2016

n=2016-1

n=2015

Vế trái là 

S=1/2+1/6+1/12+1/20+..+1/x(x+1)

S=1/1.2+1/2.3+1/3.4+1/4.5+...+1/x.(x+1)

S=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/x.(x+1)

S=1-1/(x+1)=Vế phải=2015/2016

<=>1-1/(x+1)=2015/2016

1/(x+1)=1/2016

=>x+1=2016

x=2015

Ủng hộ mk mha Chí Tiến

\(\frac{x+2015}{5}+\frac{x+2016}{4}=\frac{x+2017}{3}+\frac{x+2018}{2}\)

\(\Leftrightarrow\left(\frac{x+2015}{5}+1\right)+\left(\frac{x+2016}{4}+1\right)=\left(\frac{x+2017}{3}+1\right)+\left(\frac{x+2018}{2}+1\right)\)

\(\Leftrightarrow\frac{x+2020}{5}+\frac{x+2020}{4}-\frac{x+2020}{3}-\frac{x+2020}{2}=0\)

\(\Leftrightarrow\left(x+2020\right)\left(\frac{1}{5}+\frac{1}{4}-\frac{1}{3}-\frac{1}{2}\right)=0\)

\(\Leftrightarrow x+2020=0\)vì \(\frac{1}{5}+\frac{1}{4}+\frac{1}{3}+\frac{1}{2}\ne0\)

\(\Leftrightarrow x=-2020\)

khó lắm

bây h thì bạn giải đc chưa

Cảm ơn bạn rất nhiều mình đã hiểu rồi 

Chúc bạn học tốt nhé

\(\left(4.x-15\right)^{2016}=\left(4.x-15\right)^{2015}\)

=>\(\left(4.x-15\right)^{2016}-\left(4.x-15\right)^{2015}=0\)

=>\(\left(4.x-15\right)^{2015}.\left[\left(4.x-15\right)-1\right]=0\)

=>\(\hept{\begin{cases}\left(4.x-15\right)^{2015}=0\\\left(4.x-15\right)-1=0\end{cases}}\)=>\(\hept{\begin{cases}4x-15=0\\4.x-15-1=0\end{cases}}\)=>\(\hept{\begin{cases}4x=15\\4x=16\end{cases}}\)

=>\(\hept{\begin{cases}x=\frac{15}{4}\\x=4\end{cases}}\)

Vậy.................

(4x - 15)²⁰¹⁶ = (4x - 15)²⁰¹⁵

(4x - 5)²⁰¹⁶ - (4x - 15)²⁰¹⁵ = 0

(4x - 5)²⁰¹⁵.(4x - 15) - (4x - 15)²⁰¹⁵ = 0

(4x - 5)²⁰¹⁵.[(4x - 15) - 1] = 0

=> \(\orbr{\begin{cases}\left(4x-5\right)^{2015}=0\\\left(4x-15\right)-1=0\end{cases}}\)=>\(\orbr{\begin{cases}4x-15=0\\4x-15=1\end{cases}}\)

=> \(\orbr{\begin{cases}4x=15\\4x=16\end{cases}}\)=>\(\orbr{\begin{cases}x=\frac{15}{4}\\x=4\end{cases}}\)

bn l-ike cho mk trước đã

Ta có : A=20/11×13 + 20/13×15 +20/15×17+...+20/53×55

A = 10 ×( 2/11×13+2/13×15+...12/53×55)

A = 10 ×(1/11-1/13+1/13-1/15+1/15-1/17+...+1/53-1/55)

A = 10 × (1/11-1/55)

A =10 × 4/55

A = 8/11

\(\left|x-1\right|+\left(y+2\right)^{20}=0\)

=>x-1=0 và y+2=0

=>x=1 và y=-2

Thay x=1 và y=-2 vào X, ta được:

\(X=2\cdot1^5-5\cdot\left(-2\right)^3+2015\)

\(=2017+40=2057\)

180 - ( x + 15 ) : x x 20 = 100

( x + 15 ) : x x 20 = 80 

( x + 15 ) : x = 4

x : x + 15/x = 4

1 + 15/x = 4

15/x = 3

x = 5

\(2015-\left|x-2015\right|=x\)

\(\Leftrightarrow\left|x-2015\right|=2015-x\)

\(\Leftrightarrow\orbr{\begin{cases}x-2015=2015-x\\x-2015=-\left(2015-x\right)\end{cases}}\)

\( TH1:x-2015=2015-x\)

\(\Leftrightarrow2x=4030\)

\(\Leftrightarrow x=\frac{4030}{2}\)

\(\Leftrightarrow x=2015\)

\(TH2:x-2015=-\left(2015-x\right)\)

\(\Leftrightarrow x-2015=x-2015\)

Vậy x = 2015