cau hỏi tương tự ko có mà!!!!!!!!!!!!!!!!!!!!!!!!!!!!

3C=1.2.3+2.3.(4-1)+3.4.(5-2)+...+2014.2015.(2016-2013)

3C=2014.2015.2016

C=2014.2015.2016:3

Đặt S = 1.2 + 2.3 + 3.4 + ... + 2013.2014 
3S = 1.2.3 + 2.3.3 + 3.4.3 + ... + 2013.2014.3 
Mà : 
1.2.3 = 1.2.3 
2.3.3 = 2.3.4 - 2.3.1 
3.4.3 = 3.4.5 - 3.4.2 
................................... 
................................... 
2012.2013.3 = 2012.2013.2014 - 2012.2013.2011 
2013.2014.3 = 2013.2014.2015 - 2013.2014.2012 
Cộng tất cả, vế theo vế ---> 3S = 2013.2014.2015 
---> S = 2013.2014.2015 / 3 = 2723058910

A=1.2+2.3+3.4+4.5+...+2014.2015

=>3A=1.2.3+2.3.3+3.4.3+4.5.3+...+2014.2015.3

=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+4.5.(6-3)+...+2014.2015.(2016-2013)

=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+4.5.6-3.4.5+...+2014.2015.2016-2013.2014.2015

=(1.2.3-1.2.3)+(2.3.4-2.3.4)+(3.4.5-3.4.5)+(4.5.6-4.5.6)+...+(2013.2014.2015-2013.2014.2015)+0.1.2+2014.2015.2016

=0+2014.2015.2016

=>A=\(\frac{2014.2015.2016}{3}\)

TẠi sao lại có số 1 ở đầu vậy?    

 Đặt A = 1 + 2 + 3 + 4 + ....... + 2014

Số các số hạng của A là:

2014 - 1  + 1 = 2014 (số)

A = 2014.(2014 + 1):2 = 2029105

Đặt B = 1.2 + 2.3 + 3. 4 + .....+ 2014.2015

3B = 1.2.3 + 2.3.3 + .3.4.3 + ......... + 2014.2015

3B = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) + .......... + 2014.2015.(2016 - 2013)

3B = 1.2.3 + 2.3.4 - 1.2.3 + ........+2014.2015.2016 - 2013.2014.2015

3B = 2014 . 2015 .2016 = 8181351360

B = 8181351360 : 3

B = 2727117120

Vậy D = A + B = 2029105 + 2727117120 = 2729146225

\(A=4\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2014}-\dfrac{1}{2015}\right)\)

\(=4\cdot\dfrac{2014}{2015}=\dfrac{8056}{2015}\)

\(S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.......+\frac{1}{2015.2016}\)

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

\(S=\frac{1}{1}-\frac{1}{2016}=\frac{2015}{2016}\)

làm r sao cứ đăng hoài vậy?

S=1/1-1//2+1/2-1/3+1/3-1/4+.......=1/2014-1/2015

S=1/1-1/2015

S=2015/2015-1/2015

S=2014/2015

`A=4/(1.2)+4/(2.3)+4/(3.4)+......+4/(2014.2015)`
`=4(1/(1.2)+1/(2.3)+1/(3.4)+......+1/(2014.2015))`
`=4(1-1/2+1/2-1/3+1/3-1/4+....+1/2014-1/2015)`
`=4(1-1/2015)`
`=4. 2014/2015`
`=8056/2015`

A=4.(1/1.2+1/2.3+...+1/2014.2015)

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

A=4.(1-1/2015)

A=4.2014/2015

A=8056/2015

Giải:

\(A=\dfrac{4}{1.2}+\dfrac{4}{2.3}+\dfrac{4}{3.4}+...+\dfrac{4}{2014.2015}\) 

\(A=4.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2014.2015}\right)\) 

\(A=4.\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2014}-\dfrac{1}{2015}\right)\) 

\(A=4.\left(\dfrac{1}{1}-\dfrac{1}{2015}\right)\) 

\(A=4.\dfrac{2014}{2015}\) 

\(A=\dfrac{8056}{2015}\)

\(A=\frac{4}{1.2}+\frac{4}{2.3}+\frac{4}{3.4}+...+\frac{4}{2014.2015}\)

\(\Leftrightarrow\frac{1}{4}A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2014.2015}\)

\(\Leftrightarrow\frac{1}{4}A=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2014}-\frac{1}{2015}\)

\(\Leftrightarrow\frac{1}{4}A=\frac{1}{1}-\frac{1}{2015}\)

\(\Leftrightarrow\frac{1}{4}A=\frac{2014}{2015}\)

\(\Leftrightarrow A=\frac{2014}{2015}\div\frac{1}{4}\)

\(\Leftrightarrow A=\frac{8056}{2015}\)