Question

[Vo Thanh Anh]

s=1*2+2*3+3*4+....+101*102

Answer 1

[Arima Kousei]

\(S=1.2+2.3+3.4+...+101.102\)

\(\Leftrightarrow3S=1.2.3+2.3.3+3.4.3+...+101.102.3\)

\(\Leftrightarrow3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+101.102.\left(103-100\right)\)

\(\Leftrightarrow3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+101.102.103-100.101.102\)

\(\Leftrightarrow3S=\left(1.2.3-1.2.3\right)+\left(2.3.4-2.3.4\right)+...+\left(100.101.102-100.101.102\right)\)

\(+101.102.103\)

\(\Leftrightarrow3S=101.102.103\)

\(\Leftrightarrow S=\frac{101.102.103}{3}\)

\(\Leftrightarrow S=353702\)

Vậy \(S=353702\)

Answer 2

[Nguyệt]

nhân 3S lên là tính dc