Question

Answer 1

\(A=3^2+3^3+3^4+...+3^{24}+3^{25}\\ =\left(3^2+3^3+3^4+3^5\right)+\left(3^6+3^7+3^8+3^9\right)+...+\left(3^{22}+3^{23}+3^{24}+3^{25}\right)\\ =3^2.\left(1+3+9+27\right)+3^6.\left(1+3+9+27\right)+...+3^{22}.\left(1+3+9+27\right)\\ =40.3^2+40.3^6+...+40.3^{22}\\ =40.\left(3^2+3^6+...+3^{22}\right)⋮40\)

Answer 2

\(A=3^2\left(1+3+3^2+3^3\right)+3^6\left(1+3+3^2+3^3\right)+...+3^{22}\left(1+3+3^2+3^3\right)\)

\(=40\left(3^2+3^6+...+3^{22}\right)⋮40\)