Cho A = 1.3 + 2.4 + 3.5 +...+ 2013.2015
Tính A
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
b: 6B=2*4*6+4*6*6+6*8*6+...+46*48*6+48*50*6
=2*4*6-2*4*6+4*6*8-4*6*8+...-44*46*48+46*48*50-46*48*50+48*50*52
=48*50*52
=>B=20800
d: 9D=1*4*9+4*7*9+...+46*49*9
=1*4*2+1*4*7-1*4*7+1*7*10-1*7*10+...+46*49*52-46*49*43
=1*2*4+46*49*52
=117216
=>D=13024
a: 
Ta có: \(A=1\cdot3+2\cdot4+\cdots+99\cdot101\)
\(=1\left(1+2\right)+2\left(2+2\right)+\cdots+99\left(99+2\right)\)
\(=\left(1^2+2^2+\cdots+99^2\right)+2\left(1+2+\cdots+99\right)\)
\(=\frac{99\left(99+1\right)\left(2\cdot99+1\right)}{6}+2\cdot\frac{99\cdot\left(99+1\right)}{2}\)
\(=\frac{99\cdot100\cdot199}{6}+99\cdot100=33\cdot50\cdot199+99\cdot100\)
\(=33\cdot50\cdot\left(199+3\cdot2\right)=33\cdot50\cdot205=338250\)
A = 1.3 + 2.4 + 3.5 + ... + 99.101
A = 1.(2 + 1) + 2.(3 + 1) + 3.(4 + 1) + ... + 99.(100 + 1)
A = 1.2 + 1 + 2.3 + 2 + 3.4 + 3 + ... + 99.100 + 99
A = (1.2 + 2.3 + 3.4 + ... + 99.100) + (1 + 2 + 3 + ... + 99)
A = 333300 + 4950
a = 338250
ban chi can nhan vao day https://olm.vn/hoi-dap/question/184646.html
A=1.3+2.4+3.5+..........+99.101
A=(2-1).(2+1)+(3-1).(3+1)+......+(100-1).(100+1)
A=2^2-1+3^2-1+..........+100^2-1
A=(2^2+3^2+4^2+..........+100^2)-(1+1+........+1)
A=(2^2+3^2+4^2+..........+100^2)-99
Còn lại bạn tự làm nha
= 1.( 2 + 1 ) + 2 ( 3 + 1 ) + 3( 4 + 1 ) + ..... + 98( 99 + 1 )
= 1 . 2 + 1 + 2 . 3 + 2 + 3 . 4 + 3 + ...... 98 . 99 + 98
= ( 1 . 2 + 2 . 3 + 3 . 4 + ..... + 98 . 99 ) + ( 1 + 2 + 3 + ..... + 98 )
= 323400 + 4851
= 328351
Ta có: \(A=\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\cdot\ldots\cdot\left(1+\frac{1}{2017\cdot2019}\right)\)
\(=\left(1+\frac{1}{\left(2-1\right)\left(2+1\right)}\right)\left(1+\frac{1}{\left(3-1\right)\left(3+1\right)}\right)\cdot\ldots\cdot\left(1+\frac{1}{\left(2018-1\right)\left(2018+1\right)}\right)\)
\(=\frac{2^2-1+1}{\left(2-1\right)\left(2+1\right)}\cdot\frac{3^2-1+1}{\left(3-1\right)\left(3+1\right)}\cdot\ldots\cdot\frac{2018^2-1+1}{\left(2018-1\right)\left(2018+1\right)}\)
\(=\frac{2^2}{1\cdot3}\cdot\frac{3^2}{2\cdot4}\cdot\ldots\cdot\frac{2018^2}{2017\cdot2019}=\frac{2\cdot3\cdot\ldots\cdot2018}{1\cdot2\cdot\ldots\cdot2017}\cdot\frac{2\cdot3\cdot\ldots\cdot2018}{3\cdot4\cdot\ldots\cdot2019}\)
\(=\frac{2018}{1}\cdot\frac{2}{2019}=\frac{4036}{2019}<\frac{4038}{2019}\)
=>A<2
A = 1.3 + 2.4 + 3.5 + 4.6 + 5.7 + .. + 2013.2015 = [1.3 + 3.5+..+2013.2015] + [2.4 + 4.6 + .. + 2012.2014] = X + Y
X = 1.3 + 3.5 + 5.7 + .. + 2013.2015
X.6 = 1.3.﴾5 ‐ ﴾‐1﴿﴿ + 3.5.﴾7 ‐ 1﴿ + 5.7.﴾9‐3﴿ + 7.9.﴾11‐5﴿ + .. + 2011.2013.﴾2015‐2009﴿ + 2013.2015.﴾2017‐2011﴿
= ‐﴾‐1﴿.1.3 + 1.3.5 + 3.5.7 ‐ 1.3.5 + 5.7.9 ‐ 3.5.7 + .... = 1.3 + 2013.2015.2017
=> X = 1/6*﴾3 + 2013.2015.2017﴿ = 1363557553
tương tự Y = 2.4 + 4.6 + .. + 2012.2014
Y.6 = 2.4.6 + 4.6.﴾8‐2﴿ +... + 2012.2014.﴾2016‐2010﴿ = 2012.2014.2016
=> Y = 2012.2014.2016/6 = 1361528448
=> A = X + Y = 2725086001
lâu ko làm nên sai hay đúng thì mình ko biết nữa
face you