Question

Tính:

1*2+2*3+3*4+4*5+...+99*100

ai nhanh mk tjk nha 

Answer 1

Đặt A=1.2+2.3+...+99.100

3A=1.2.3+2.3.3+...+99.100.3

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

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

=99.100.101-0.1.2

=99.100.101

=>\(A=\frac{99.100.101}{3}=333300\)

Answer 2

Đặt \(A=1.2+2.3+3.4+4.5+...+99.100\)\(\Rightarrow3.A=1.2.3+2.3.3+3.4.3+4.5.3+...+99.100.3\)\(=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+4.5.\left(6-3\right)+...+99.100.\left(101-98\right)\)

\(=1.2.3+2.3.4-1.2.3+3.4.-2.3.4+4.5.6+3.4.5+...+\)\(99.100.101-98.99.100\)

\(=99.100.101\)

\(=999900\Rightarrow B=999900\div3=333300\)

Chưa chắc lắm đâu nha !