Question

Tính tổng A=1.2+2.3+3.4+...+2013.2014

Answer 1

\(A=1.2+2.3+...+2013.2014\\ \Rightarrow3A=1.2.3+2.3.3+...+2013.2014.3\\ \Rightarrow3A=1.2.3+2.3.\left(4-1\right)+...+2013.2014.\left(2015-2012\right)\\ \Rightarrow3A=1.2.3+2.3.4-1.2.3+...+2013.2014.2015-2012.2013.2014\\ \Rightarrow3A=2013.2014.2015\\ \Rightarrow A=\dfrac{2013.2014.2015}{3}\)

Answer 2

Tham Khảo :

 A = 1.2 + 2.3 + 3.4 + ... + 2013.2014 
3A = 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 
---> A = 2013.2014.2015 / 3 = 2723058910

Answer 3

A= 1xx2 + 2xx3 + 3xx4 + ... + 2013xx2014
`3xxA = 1xx2xx3 +2xx3xx3 +3xx4xx3+ ... + 2013xx2014xx3`
`3xxA = 1xx2xx(3-0)+2xx3xx(4-1)+3xx4xx(5-2)+...+2013xx2014xx(2015-2012)`
`3xxA = 1xx2xx3+2xx3xx4-1xx2xx3+3xx4xx5-2xx3xx4+...+2013xx2014xx2015-2012xx2013xx2014`
`3xxA=(2013xx2014xx2015) : 3`
`A = 2723058910`