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Which series is convergent? Check all that apply.

Which series is convergent? Check all that apply.-example-1
User Blockhead
by
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1 Answer

3 votes

Answer:

The convergent series are;


\sum \limits _(n = 1)^\infty \left( (1)/(5) \right) ^n

(And)


\sum \limits _(n = 1)^\infty \left( (1)/(10) \right) ^n

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 (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 (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( (1)/(5) \right) ^n

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

Fourth option


\sum \limits _(n = 1)^\infty \left( (1)/(10) \right) ^n

As 'n' increases,
3 *\left( (1)/(10) \right) ^n, becomes more smaller and tend to '0', therefore, the series converges

Fifth option


\sum \limits _(n = 1)^\infty (1)/(10) \cdot (3) ^n

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

User Seanyboy
by
7.5k points
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