Question

Which series is convergent? Check all that apply.

Answer 1

Answer:

The convergent series are;

$\sum \limits _{n = 1}^\infty \left( \dfrac{1}{5} \right) ^n$

(And)

$\sum \limits _{n = 1}^\infty \left( \dfrac{1}{10} \right) ^n$

Step-by-step explanation:

A series in mathematics is the sum of a sequence of numbers to infinity

A convergent series is a series that sums to a limit

From the given options, we have;

First option

$\sum \limits _{n = 1}^\infty \dfrac{2\cdot n}{n + 1}$

As 'n' increases, 2·n becomes more larger than n + 1, and the series diverges

Second option

$\sum \limits _{n = 1}^\infty \dfrac{n^2 - 1}{n - 2}$

As 'n' increases, n² - 1, becomes more larger than n - 2, and the series diverges

Third option

$\sum \limits _{n = 1}^\infty \left( \dfrac{1}{5} \right) ^n$

As 'n' increases, $\left( \dfrac{1}{5} \right) ^n$, becomes more smaller and tend to '0', therefore, the series converges

Fourth option

$\sum \limits _{n = 1}^\infty \left( \dfrac{1}{10} \right) ^n$

As 'n' increases, $3 \times\left( \dfrac{1}{10} \right) ^n$, becomes more smaller and tend to '0', therefore, the series converges

Fifth option

$\sum \limits _{n = 1}^\infty \dfrac{1}{10} \cdot (3) ^n$

As 'n' increases, $\dfrac{1}{10} \cdot (3) ^n$, becomes more larger and tend to infinity, therefore, the series diverges.

Answer 2

Answer:

C and D

Step-by-step explanation:

Edge 2021