Question

biết rằng \(1^2+2^2+3^2+...+10^2=385\) hãy tính nhanh tổng sau :

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

Answer 1

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

\(A=\left(1.100\right)^2+\left(2.100\right)^2+\left(3.100\right)^2+...+\left(10.100\right)^2\)

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

\(A=10000.385=3850000\)

vậy \(A=3850000\)

Answer 2

Ta có:A=100²+200²+300²+...+1000²

=100².1²+100².2²+100².3²+...+100².10²

=100²(1²+2²+3²+...10²)

=10000.385

=3850000

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