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

Answer:

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

Step-by-step 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.