Ta có:
\(S=1.2.3+2.3.4+3.4.5+...+98.99.100\)
\(\Rightarrow4S=1.2.3.4+2.3.4.\left(5-1\right)+...+98.99.100.\left(101-97\right)\)
\(\Rightarrow4S=1.2.3.4++2.3.4.5-1.2.3.4+...+98.99.100.101-97.98.99.100\)
\(\Rightarrow4S=98.99.100.101\)
\(\Rightarrow S=\dfrac{98.99.100.101}{4}=24497550\)
Vậy \(S=24497550\)
Ta có:
\(S=1.2.3+2.3.4+...+98.99.100\\ \Rightarrow4S=1.2.3.4+2.3.4.4+...+98.99.100.4\\ 4S=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)\\ +...+98.99.100.\left(101-97\right)\\ 4S=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5\\ +...+98.99.100.101-97.98.99.100\\ \Leftrightarrow4S=\left(1.2.3.4-1.2.3.4\right)\\ +\left(2.3.4.5-2.3.4.5\right)+\\ \left(3.4.5.6-3.4.5.6\right)+...+\\ \left(97.98.99.100-97.98.99.100\right)+98.99.100.101\\ \Rightarrow4S=98.99.100.101\\ \Rightarrow S=\dfrac{98.99.100.101}{4}\\ \Rightarrow S=24497550\)
