Question

Tính nhanh:

(1000 - 1³ ) . (1000 - 2³) . (1000 - 3³) . ... . (1000 - 15³)

Answer 1

\(\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right)...\left(1000-15^3\right)\)

\(=\left(1000-1^3\right)\left(1000-2^3\right)...\left(1000-10^3\right)....\left(1000-15^3\right)\)

\(=\left(1000-1^3\right)\left(1000-2^3\right)...\left(1000-1000\right)....\left(1000-15^3\right)\)

\(=\left(1000-1^3\right)\left(1000-2^3\right)....0.....\left(1000-15^3\right)\)

\(=0\)

Answer 2

\(\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right).....\left(1000-15^3\right)\)

\(=\left(1000-1^3\right)\left(1000-2^3\right)\left(1000-3^3\right)....\left(1000-15^3\right)\left(1000-10^3\right)\)\(=A.\left(1000-10^3\right)\)

\(=A.0=0\)

Answer 3

Theo quy luật của dãy số ta có thừa số :

\(\left(1000-10^3\right)=\left(1000-1000\right)=0\)

\(\Rightarrow\left(1000-1^3\right)\left(1000-2^3\right)...\left(1000-10^3\right)...\left(1000-15\right)=0\)