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:
Ta đặt \(A=1.3+3.5+5.7+...+99.101\)
\(\Rightarrow6A=1.3.\left(5+1\right)+3.5.\left(7-1\right)+5.7.\left(9-3\right)+...+99.101.\left(103-97\right)\)
\(\Rightarrow6A=1.3.5+1.3+3.5.7-1.3.5+5.7.9-3.5.7+...+99.101.103-97.99.101\)
\(\Rightarrow6A=3+99.101.103\)
\(\Rightarrow6A=1029900\)
\(\Rightarrow A=1029900:6=171650\)
