Question

Tinh: A= 1.3 + 3.5 + 5.7 + ...+ 97.99

Answer 1

\(A=1.3+3.5+5.7+...+97.99\)

\(\Rightarrow6A=1.3.6+3.5.\left(7-1\right)+5.7.\left(9-3\right)+...+97+99.\left(101-95\right)\)

\(\Rightarrow6A=1.3.6+3.5.7-1.3.5+5.7.9-3.5.7+...+97.99.101-95.97.99\)

\(\Rightarrow6A=1.3.6+97.99.101-1.3.5\)

\(\Rightarrow6A=3.\left(1+97.33.101\right)\)

\(\Rightarrow2A=1+323301\)

\(\Rightarrow2A=323302\)

\(\Rightarrow A=161651\)