Ta có: A=1.2.3+2.3.4+…+98.99.100
=>A.4=1.2.3.4+2.3.4.4+…+98.99.100.4
=>A.4=1.2.3.(4-0)+2.3.4.(5-1)+…+98.99.100.(101-97)
=>A.4=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+…+98.99.100.101-97.98.99.100
=>A.4=98.99.100.101
=>A.4=97990200
=>A=97990200:4
=>A=24497550
CT:
1.2.3...a+2.3.4...(a+1)+......+(n+1)(n+2)....(n+a)
=\(\frac{\left(n+1\right)\left(n+2\right).....\left(n+a+1\right)}{a+1}\)