Question

a, Tính tổng

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

Answer 1

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

3A=3.(1.2+2.3+3.4+...+99.100)

3A=3.1.2+3.2.3+3.3.4+....+3.99.100

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

3A=1.2.3+2.3.4- 1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100

3A=99.100.101

A=\(\dfrac{99.100.101}{3}\)

Answer 2

Ta có :

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

\(\Leftrightarrow3A=1.2.3+2.3.3+...........+99.100.3\)

\(\Leftrightarrow3A=1.2.3+2.3.\left(4-1\right)+......+99.100.\left(101-98\right)\)

\(\Leftrightarrow3A=1.2.3+2.3.4-1.2.3+.....+99.100.101-98.99.100\)

\(\Leftrightarrow3A=99.100.101\)

\(\Leftrightarrow A=\dfrac{99.100.101}{3}=333300\)