Question

PLEASE HELPP 64, 16, 4, 1 converging or diverging

Answer 1

Answer:

The series 64, 16, 4, 1 is convergent.

Step-by-step explanation:

Let be $\{x_{1}, x_{2},...,x_{n}\}$ the set of values of the series. A series is convergent if and only if:

$\frac{x_{i + 1}}{x_{i}} < 1, \, \forall\,i\in \mathbb{N}$ (1)

If we know that $x_{1} = 64$, $x_{2} = 16$, $x_{3} = 4$ and $x_{4} = 1$, then the convergence ratio of each pair of consecutive values are, respectively:

$\frac{x_{2}}{x_{1}} = \frac{1}{4}$, $\frac{x_{3}}{x_{2}} = \frac{1}{4}$, $\frac{x_{4}}{x_{3}} = \frac{1}{4}$

Hence, the series 64, 16, 4, 1 is convergent.