Question

1.3+3.5+5.7+...+99.101

Answer 1

Đặt A = 1.3+3.5+5.7+ ...+ 99.101

ta có : 6A = 1.3.6+3.5.6+5.7.6 +...+99.101.6

               = 1.3.(5+1) + 3.5.( 7-1) +5.7.(9-3) +...+99.101.(103-97)

               =1.3.5+1.3+3.5.7-1.3.5+5.7.9-3.5.7+...+99.101.103-97.99.101

               =1.3+99.101.103

              A =1029900 :6 = 171650   

Answer 2

Answer:

Ta đặt \(A=1.3+3.5+5.7+...+99.101\)

\(\Rightarrow6A=1.3.\left(5+1\right)+3.5.\left(7-1\right)+5.7.\left(9-3\right)+...+99.101.\left(103-97\right)\)

\(\Rightarrow6A=1.3.5+1.3+3.5.7-1.3.5+5.7.9-3.5.7+...+99.101.103-97.99.101\)

\(\Rightarrow6A=3+99.101.103\)

\(\Rightarrow6A=1029900\)

\(\Rightarrow A=1029900:6=171650\)