Question

Tính nhanh:

1.2+ 2.3+ 3.4+ ...+ 98.99

Answer 1

Đặt :

\(A=\)\(1.2+2.3+3.4+.................+98.99\)

\(\Rightarrow3A=1.2.3+2.3.3+3.4.3+...............+98.99.3\)

\(\Rightarrow3A=1.2.\left(3-0\right)+2.3.\left(4-1\right)+3.4.\left(5-2\right)+.................+98.99.\left(100-97\right)\)

\(\Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+................+98.99.100-97.98.99\)\(\Rightarrow A=\dfrac{98.99.100}{3}=323400\)

Answer 2

Đặt A=1.2+ 2.3+ 3.4+ ...+ 98.99

3A=1.2.3+ 2.3.3+ 3.4.3+ ...+ 98.99.3

3A=1.2.3+2.3.(4-1)+3.4.(5-2)+...+98.99.(100-97)

3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+98.99.100-97.98.99

3A=98.99.100

A=98.99.100\(\div\)3

A=323400