$$x = \sum\limits_{n = 0}^\infty {{a^n},y = \sum\limits_{n = 0}^\infty {{b^n},z = \sum\limits_{n = 0}^\infty {{c^n}} } } $$, where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc $$\ne$$ 0, then :

If $$A = \sum\limits_{n = 1}^\infty {{1 \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}} $$ and $$B = \sum\limits_{n = 1}^\infty {{{{{( - 1)}^n}} \over {{{\left( {3 + {{( - 1)}^n}} \right)}^n}}}} $$, then $${A \over B}$$ is equal to :

The sum 1 + 2 . 3 + 3 . 3² + ......... + 10 . 3⁹ is equal to :

Let x, y > 0. If x³y² = 2¹⁵, then the least value of 3x + 2y is