Question

Sa se rezolve prin inductie
1³+3³+...+(2n-1)³=?

Answer 1

$1^3 = 1\\ 1^3+3^3 = 1+27 = 28 = \boxed{4\cdot 7}= 2^2\cdot (2\cdot 2^2-1)\\ 1^3+3^3+5^3 = 153 = \boxed{9\cdot 17} = 3^2\cdot (2\cdot 3^2-1)\\ 1^3+3^3+5^3+7^3 = 496 = \boxed{16\cdot 31} = 4^2\cdot (2\cdot 4^2-1)\\1^3+3^3+5^3+7^3+9^3 = 1225 = \boxed{25\cdot 49} = 5^2\cdot (2\cdot 5^2-1)\\\\ \vdots \quad \text{(Analog)}\\\\ 1^3+3^3+5^3+...+(2n-1)^3 = \boxed{n^2\cdot(2n^2-1)}\quad \checkmark$