Question

Consider the series 1/4+1/6+1/9+2/27+4/81+....

Does the series converge or diverge?


Select answers from the drop-down menus to correctly complete the statements.

Answer 1

The series converges as any two consecutive elements of the sum are monotonically decreasing.

Explanation:

The series converges since the consecutive element is monotonically decreasing. That is:

`\forall\,i\in \mathbb{N}\,a_(i) > a_(i+1)` (1)

Where:

`a_(i)` - The i-th component of the sum.

`a_(i+1)` - The (i+1)-th component of the sum.