Question

Tính tổng : S = 1 . 2+ 2 . 3 + 3 . 4 + ....... + 99 . 100

Answer 1

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

\(\Rightarrow3S=1.2.3+2.3.3+3.4.3+...+99.100.3\)

\(\Rightarrow3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+99.100.\left(101-98\right)\)

\(\Rightarrow3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)

\(\Rightarrow3S=99.100.101=999900\Rightarrow S=999900\div3=333300\)

Vậy : \(S=333300\)

Answer 2

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

\(3S=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)\)

\(3S=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100\)

\(3S=99.100.101=999900\)

\(S=999900:3\)

\(\Rightarrow S=333300\)