Question

Tính A=\(1.3^2+3.5^2+5.7^2+...+97.99^2\)

 

Answer 1

A=1.3.(5-2)+3.5.(7-2)+5.7.(9-2)+...+97.99(101-2)=

=(1.3.5+3.5.7+5.7.9+...+97.99.101) - 2.(1.3+3.5+5.7+...+97.99)

Đặt 

B=1.3.5+3.5.7+5.7.9+...+97.99.101

=> 8B=1.3.5.8+3.5.7.8+5.7.9.8+...+97.99.101.8=

=1.3.5(7+1)+3.5.7.(9-1)+5.7.9.(11-3)+...+97.99.101.(103-95)=

=1.3.5+1.3.5.7-1.3.5.7+3.5.7.9-3.5.7.9+5.7.9.11-...-95.97.99.101+97.99.101.103=

=3.5+97.99.101.103

\(\Rightarrow B=\dfrac{15+97.99.101.103}{8}\)

Đặt 

C=1.3+3.5+5.7+...+97.99

=> 6C=1.3.6+3.5.6+5.7.6+...+97.99.6=

=1.3.(5+1)+3.5.(7-1)+5.7.(9-3)+...+97.99.(101-95)=

=1.3+1.3.5-1.3.5+3.5.7-3.5.7+5.7.9-...-95.97.99+97.99.101=

=1.3+97.99.101

\(\Rightarrow C=\dfrac{3+97.99.101}{6}\)

\(\Rightarrow A=B-2C\)

Thay các giá trị của B và C bạn tự tính nốt nhé