\(F=1.100+2.99+3.98+...+99.2+1.100\)
\(=1.100+2.\left(100-1\right)+3.\left(100-2\right)+....+100.\left(100-99\right)\)
\(=1.100+2.100-2.1+3.100-3.2+...+100.100-100.99\)
\(=100.\left(1+2+3+...+100\right)-\left(1.2+2.3+3.4+....99.100\right)\)
\(=100.\frac{101.100}{2}-\frac{99.100.101}{3}=505000-333300=171700\)
Đúng thì ủng hộ nha!
F = 1.100 + 2.(100-1) + 3. (100-2) +...+100.(100-99)
F = 1.100 + 2.100 - 1.2 + 3.100 - 2.3 + ...+ 100.100 - 99.100
F = 100 . ( 1+2+3+...+100) - (1.2+2.3+3.4+...+99.100)
= 100.(101.100:2) - (99.100.101:3) = 505000 - 333300 = 17100
