Question

Biết rằng 1²+2²+3²+...+10²=385. Hãy tính nhanh tổng sau: 

A= 100²+200²+300²+...+1000²

Answer 1

\(A=100^2+200^2+300^2+...+1000^2\)

=>\(A=100^2\left(1^2+2^2+3^2+...+10^2\right)\)

=>\(A=10000.385\)

=>\(A=3850000\)

Answer 2

\(A=100^2+200^2+300^2+......+1000^2\)

\(=1000^2\left(1^2+2^2+3^2+...+10^2\right)\)

\(=10000.385\\\)

\(=3850000\)