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

=> 3S = 2013.2014.2015

=> A = 2013.2014.2015 / 3 = 2723058910

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

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

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

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

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

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

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

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

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

đơn giản

S=1.2+2.3+3.4+....+99.100

3S = 1.2.3 + 2.3.3 + 3.4.3+...... + 99.100.3

3S = 1.2.3 + 2.3.(4-1) + 3.4.(5-2) +.....+  99.100.(101-98)

3S = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4+..... + 99.100.101 - 98.99.100

3S = 99.100.101

S = \(\frac{99.100.101}{3}=333300\)

A = 1.2+2.3+3.4+......+99.100 

A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3 
A . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98) 
A . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100 
A . 3 = 99.100.101 
A = 99.100.101 : 3 
A = 33.100.101 
A = 333 300

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

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 .

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

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

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

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

ta chia S đó ra thành 2 S 

cách chia như sao:

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

<=>S=(1+2+3+4+...+2014).(2+3+4+5+...+2015) rồi ta chia ra 2 S

S=(1+2+3+4+...+2014)vàS=(2+3+4+5+...+2015)

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