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 1/3.4+1/4.5+1/5.6+...+1/99.100

=1/3-1/4+1/4-1/5+1/5-1/6+...+1/98-1/99+1/99-1/100

=1/3-1/100

=97/300

\(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+...+\frac{1}{99.100}\)

\(=\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{99}-\frac{1}{100}\)

\(=\frac{1}{3}-\frac{1}{100}\)

\(=\frac{97}{300}\)

1/3.4 + 1/ 4.5 + 1/5.6 + ... + 1/99.100

= 1/3 - 1/4 + 1/4 - 1/5 + 1/5 - 1/6 + ... + 1/99 - 1/100

= 1/3 -1/100

= 97/300

5E= 3.4.5+ 4.5.(6-1)+5.6.(7-2)+...+99.100.(101-96)

A = 1.2 + 2.3 + 3.4 + ....... + 99.100

3A = 1.2.3 + 2.3.3 + 3.4.3 + ....... + 99 . 100 . 3

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

3A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ..... + 99 . 100 . 101 - 98 . 99 . 100

3A = (1.2.3 - 1.2.3) + (2.3.4-2.3.4) + ... + (98.99.100 - 98.99.100) + 99  . 100 . 101

3A = 99 . 100 . 101 = 999900

A = 999900 : 3 = 333300

A=1*2+2*3+3*4+...+99*100

A=100*101*102:3

A=343400(công thức)

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gọi tổng là S ta có

3S=1.2.3-0.1.2+2.3.4-1.2.3+......+99.100.101-98.99.100

=>3S=98.99.100

=>S=\(\frac{98.99.100}{3}=323400\)

333300

A = 1.2+2.3+3.4+......+99.100 
Gấp A lên 3 lần ta có: 
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

=(99.100.101-0.1.2):3=333300

Đặt A= 1.2+2.3 +.......+99.100

3A= 1.2.3+2.3.4+3.4.3 +......+ 99.100.3

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

3A = (1.2.3 + 2.3.4 + 3.4.5 +...... + 99.100.101) - (0.1.2 + 1.2.3 + 2.3.4 +.......+ 98.99.100)

3A = 99.100.101 - 0.1.2

3A = 999900 - 0

3A= 999900

A= 999900 : 3

A = 333300

Học tốt nha!

Đặt A = 1.2 + 2.3 + ... + 99.100

=> 3A = 1.2.3 + 2.3.(4-1) + ... + 99.100.(101-98)

=> 3A = 1.2.3 + 2.3.4 - 1.2.3 + ... + 99.100.101 - 98.99.100

=> 3A = 99.100.101

=> A = 333300

A = 1.2 + 2.3 + 3.4 + 4.5 + ... + 99.100 + 100.101

3.A = 1.2.3 + 2.3.3 +3.4.3 + ... + 100.101.3

3A= 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 100.101.(102 - 99)

3A = 1.2.3 + 2.3.4 - 1.2.3 + 2.3.4 -3.4.5 + ... +99.100.101 -100.101.102

3A = 99.100.101

A = 99.100.101 : 3

A = 33.100.101

Vậy A = 33. 100 .101 (Tự tính)

A=1.2+2.3+3.4+.....+99.100+100.101

333300