có ví dụ rồi sao không tự làm

\(\left(2013.2014+2014.2015+2015.2016\right)\left(1+\frac{1}{3}-1\frac{1}{3}\right)\)

\(=\left(2013.2014+2014.2015+2015.2016\right)\left(\frac{4}{3}-\frac{4}{3}\right)\)

\(=\left(2013.2014+2014.2015+2015.2016\right).0\)

\(=0\)

ggggggggggggggggggggggggggggggg

a,\(\frac{2015.2016+2015-1}{2014+2015.2016}=\frac{2015.2016+2014}{2014+2015.2016}=1\)\(1\)

b,\(=1-\frac{1}{5}+\frac{1}{5}...-\frac{1}{2011}+\frac{1}{2011}-\frac{1}{2015}=1-\frac{1}{2015}=\frac{2014}{2015}\)

c,\(=\frac{12}{35}+\frac{12}{35}+\frac{12}{35}+\frac{12}{35}=\frac{12}{35}.4=\frac{48}{35}\)

48/35 nha

\(\frac{2014.150+1000}{151.2014-1014}\)= \(\frac{150+1000}{\left(150+1\right).1014}\)

= \(\frac{1000}{1014}\)= \(\frac{500}{507}\)

nhớ ủng hộ mik nha

a. ta có (0.1+0.19)+(0.2+0.18)......+0.10 
A=0.20+0.20++0.20+0.20+0.20+0.20+0.20+0.20+0.20+0.10
A=1.90 
câu b mình pó tay

a ) \(A=0,1+0,2+...+0,19\)

\(A=\left(0,1+0,2+...+0,9\right)+\left(0,10+0,11+...+0,19\right)\)

\(A=0,1\times\left(1+2+...+9\right)+0,1\times\left(1+1,1+...+1,9\right)\)

\(A=0,1\times45+0,1\times14,5\)

\(A=0,1\times\left(45+14,5\right)\)

\(A=0,1\times59,5\)

\(A=5,95\)

b ) \(B=\left(2017\times2016+2014\times2015\right)\times\left(1+\frac{1}{2}\div1\frac{1}{2}+1\frac{1}{3}\right)\)

\(B=\left(2017\times2016+2014\times2015\right)\times\left(1+\frac{1}{2}\div\frac{3}{2}+\frac{4}{3}\right)\)

\(B=\left(2017\times2016+2014\times2015\right)\times\left(1+\frac{2}{6}+\frac{4}{3}\right)\)

\(B=\left(2017\times2016+2014\times2015\right)\times\frac{8}{3}\)

\(A=1.2.3+2.3.4+3.4.5+....+2014.2015.2016\)

\(4A=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+....+2014.2015.2016.\left(2017-2013\right)\)\(4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+2014.2015.2016.2017-2013.2014.2015.2016\)\(4A=2014.2015.2016.2017\)

\(A=\dfrac{2014.2015.2016.2017}{4}=4215446423280\)

xét mẫu số : 151 x 2014 - 1014 

= 2014x(150+1) - 1014 

= 2014 x 150 + 2014 - 1014 

= 2014 x 150 + 1000

vậy phân số sẽ trờ thành : 2014 x 150 + 1000 / 2014 x 150 + 1000 =1 

\(\frac{2014\cdot150+1000}{151\cdot2014-1014}=\frac{2014\cdot150+1000}{\left(150+1\right)\cdot2014-1014}\)

                                   \(=\) \(\frac{2014\cdot150+1000}{2014\cdot150+2014\cdot1-1014}=\frac{2014\cdot150+1000}{2014\cdot150+2014=1014}\) 

                                      \(=\frac{2014\cdot150+1000}{2014\cdot150+1000}=1\)

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2014