Question

Tính Tổng :
\(B=1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\)
Mong Mọi Người Giúp đỡ

Answer 1

\(B=1.2+2.3+....+99.100\)

\(\Rightarrow3B=1.2.3+2.3.4+...+99.100.3\)

\(\Rightarrow3B=1.2.\left(3-0\right)+2.3.\left(4-1\right)+....+99.100.\left(101-98\right)\)

            \(=\left(1.2.3+2.3.4+....+99.100.101\right)-\left(0.1.2+1.2.3+...+98.99.100\right)\)

              \(=99.100.101-0.1.2\)

               = 999900 - 0

=> B = 999900 : 3 = 333300

Vậy B = 333300

Answer 2

B = 1.2 + 2.3 + 3.4 + ...+ 99.100

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

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

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

3B  = (1.2.3+2.3.4+...+99.100.101) - (1.2.3+...+98.99.100)

3B = 99.100.101

\(\Rightarrow B=\frac{99.100.101}{3}=333300\)

Answer 3

\(B=1.2+2.3+3.4+...+99.100\)

\(\Rightarrow3B=1.2.3+2.3.3+....+99.100.3\)

\(\Rightarrow3B=1.2.3+2.3.(4-1)+...+99.100.(101-98)\)

\(\Rightarrow3B=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100\)

\(\Rightarrow3B=99.100.101\)

\(\Rightarrow B=333300\)

Answer 4

Đặt B=1.2+2.3+3.4+...+99.100

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

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

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

3B= 99.100.101 -0.1.2

3B= 999900-0= 999900

B= 999900:3= 333300

Vậy B=333300

TK MIK NHA

Answer 5

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

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

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 = 98 . 99 . 100

B = 98 . 33 . 100 = 323400