Question

tinh A=1*4+2*5+3*6+v.v..+99*102

A=?

 

Answer 1

Ta có: A = 1 . 4 + 2 . 5 + 3 . 6 + ... + 99 . 102

= 1 . (2 + 2) + 2 . (3 + 2) + 3 . (4 + 2) + ... + 99 . (100 + 2)

= (1 . 2 + 1 . 2) + (2 . 3 + 2 . 2)  + (3 . 4 + 3 . 2) + ... + (99 . 100 + 99 . 2)

= (1 . 2 + 2 . 3 + 3 . 4 + ... + 99 . 100) + (1 . 2 + 2 . 2 + 3 . 2 + ... + 99 . 2)

Đặt B = 1 . 2 + 2 . 3 + 3 . 4 + ... + 99 . 100

3B = 1 . 2 . 3 + 2 . 3 . (4 - 1) + 3 . 4 . (5 - 2) + ... + 99 . 100 . (101 - 98)

3B = 1 . 2 . 3 + 2 . 3 . 4 - 1 . 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + ... + 99 . 100 . 101 - 98 . 99 . 100

3B = 99 . 100 . 101 

3B = 999900

B = 333300

Thay vào A ta có: A = 333300 + (1 . 2 + 2 . 2 + 3 . 2 + ... + 99 . 2) = 333300 + (1 + 2 + 3 + ... + 99) . 2 = 333300 + 99 . 100 : 2 . 2 = 333300 + 99 . 100 = 333300 + 9900 = 343200

Answer 2

A=1.(2+2)+2.(3+2)+3.(4+2)+.........+99.(100+2)

A=(1.2+1.2)+(2.3+2.2)+(3.4+3.2)+..............+(99.100+99.2)

A=1.2+2.3+3.4+........+99.100+1.2+2.2+3.2+4.2+.......+99.2

Đặt B=1.2+2.3+.........+99.100

3B=1.2.(3-0)+2.3.(4-1)+............+99.100.(101-98)

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

3B=99.100.101

3B=999900

B=333300

A=333300+(1+2+...........+99).2

A=333300+100.99:2.2

A=333300+100.99

A=333300+9900

A=343200

Answer 3

A=1.(2+2)+2.(3+2)+3.(4+2+...+99.(100+2)

A(1.2+1.2)+(2.3+2.2)+(3.4+3.2)+...+(99.100+99.2)

A=1.2+2.3+3.4+...+99.100+1.2+2.3+3.2+4.2+99.2

Dat B=1.2+2.3+...+99.100

3B=1.2.(3-0)+2.3+(4-1)+...+99.100.(101-98)

3B=1.2.3+2.3.4+...+99.1000.101-0.1.2-1.2.3-...-98.99.100

3b=99.100.101

3b=999900

B=999900:3=333300

A=333300+(1+2+...+99).2

A=333300+100.99:2.2

A=333300+100.99

A=333300+9900

A=343200