3A= 1.2.3+2.3.3+3.4.3+...........+2010.2011.3

3A=1.2.3+2.3.(4-1)+3.4.(5-2)+.........+2010.2011.(2012-2009)

=>3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+.....+2010.2011.2012-2009.2010.2011

=>3A=2010.2011.2012

=>3A=3.670.2011.2012

=>A=670.2011.2012

=>A= .......lấy máy tính mà tính

Ta có: \(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{2020\cdot2021}+\dfrac{1}{2021\cdot2022}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2020}-\dfrac{1}{2021}+\dfrac{1}{2021}-\dfrac{1}{2022}\)

\(=1-\dfrac{1}{2022}=\dfrac{2021}{2022}\)

1/1x2+1/2x3+1/3x4+...+1/2020x2021+1/2021x2022

=1/1-1/2+1/2-1/3+1/3-1/4+...+1/2020-1/2021+1/2021-1/2022.

=1/1-1/2022

=2021/2022

ai tích mình mình tích lại cho

tinh tong A= 1.2^2+2.3^2+3.4^2+........+2018.2019^2

E = 1.2+2.3+3.4+......+99.100
Gấp E lên 3 lần ta có:
E . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3
E . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)
E . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100                                                                                       E . 3 = 99.100.101
E = 99.100.101 : 3
E = 33.100.101
E = 333 300

k mik nha

E = 1.2 + 2.3 + 3.4 + ... + 99.100

=> 3E = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3

=> 3E = 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) +...+ 99.100.(101-98)

=> 3E = 1.2.3 - 0 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100

=> 3E = 99.100.101

=> E = 333300

\(S=\frac{3}{1.2}+\frac{3}{2.3}+\frac{3}{3.4}+\frac{3}{4.5}+....+\frac{3}{2015.2016}\)

\(\Rightarrow\frac{1}{3}.S=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2015.2016}\)

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

\(\Rightarrow\frac{1}{3}.S=\frac{1}{1}-\frac{1}{2016}\)

\(\Rightarrow\frac{1}{3}.S=\frac{2015}{2016}\)

\(\Rightarrow S=\frac{2015}{672}\)

Vậy: \(\Rightarrow S=\frac{2015}{672}\)

Bạn giải giúp mk câu mk đăng tầm 5 phút nha!

đơn giản

S=1/1-1/2+1/2-1/3+1/3-1/4+1\5-..............................-1/2015+1/2016

S=1/1-1/2016

S=2015/2016

Ta có : A = 1/1.2 + 1/2.3 + .... + 1/98.99 + 1/99.100 .

=>       A = 1 - 1/2 + 1/2 - 1/3 + .... + 1/98 - 1/99 + 1/99 - 1/100 .

=>       A = 1 - 1/100 .

=>       A = 99/100 .

\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{99.100}\)

\(\Rightarrow A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

\(\Rightarrow A=1-\frac{1}{100}\)

\(\Rightarrow A=\frac{99}{100}\)

Cảm ơn nhìu nha

A=330

a=49.5

Ok dễ thôi nếu như bạn tk mk