Question

Biết 13 + 23 + ...... + 103 = 3025 . Tính S = 23 + 43 + 63 + ..... + 203

Answer 1

\(1^3+2^3+3^3+...+10^3=3025\\ S=2^3+4^3+6^3+...+20^3\\ =\left(2\cdot1\right)^3+\left(2\cdot2\right)^3+\left(2\cdot3\right)^3+...+\left(2\cdot10\right)^3\\ =2^3\cdot1^3+2^3\cdot2^3+2^3\cdot3^3+...+2^3\cdot10^3\\ =2^3\left(1^3+2^3+3^3+...+10^3\right)\\ =8\cdot3025\\ =24200\)

Answer 2

Ta có:

\(S=2^3+4^3+6^3+...+20^3.\)

\(\Rightarrow S=2^3.1^3+2^3.2^3+2^3.3^3+...+2^3.10^3.\)

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

\(\Rightarrow S=8.3025=24200.\)

Vậy \(S=24200.\)