A + B = ( 1 . 99 + 2 . 98 + 3 . 97 + ... + 99 . 1 ) + ( 1 . 101 + 2 . 102 + 3 . 103 + ... + 99 . 199 )

A + B = 99 . ( 1 + 199 ) + 98 . ( 2 + 198 ) + 97 . ( 3 + 197 ) + ... + 2 . ( 102 + 98 ) + 1 . ( 99 + 101 ) 

A + B = 99 . 200 + 98 . 200 + 97 . 200 + ... + 2 . 200 + 1 . 200

A + B = ( 99 + 98 + 97 + ... + 2 + 1 ) . 200

A + B = 4950 . 200

A + B = 990000

A+B=(1.99+2.98+...+99.1)+(1.101+2.102+...+99.199)

=(1.99+1.101)+(2.98+2.102)+...+(99.1+99.199)

=1.(99+101)+2.(98+102)+...+99(1+199)

=200+2.200+...+99.200

=200.(1+2+3+4+...+99)

=200.4950

=.....

\(A = 1.99 + 2.98 + 3.97 + ...+ 97.3 + 98.2 + 99.1\)

\(A=1.99+2.\left(99-1\right)+3.\left(99-2\right)+...+98.\left(99-97\right)+99.\left(99-98\right)\)

\(A=1.99+2.99-1.2+3.99-2.3+98.99-97.98+99.99-98.99\)

\(=\left(1.99+2.99+3.99+...+98.99+99.99\right)-\left(1.2+2.3+3.4+...+97.98+98.99\right)\)

\(=99.\left(1+2+3+...+98+99\right)-\left(1.2+2.3+3.4+...+97.98+98.99\right)\)

\(=99.4950-\left(1.2+2.3+3.4+97.98+98.99\right)\)

Mà \(1.2+2.3+3.4+...97.98+98.99\)

\(=\frac{1}{3}.\left[1.2+2.3.\left(4-1\right)+3.4.\left(5-2\right)+98.99.\left(100-97\right)\right]\)

\(=\frac{1}{3}.98.99.100=323400\)

\(\Rightarrow A=99.4950-323400=166650\)