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Elis [28]
2 years ago
6

Which geometric series diverges? Three-fifths three-tenths three-twentieths StartFraction 3 Over 40 EndFraction ellipsis Negativ

e 10 4 minus eight-fifths StartFraction 16 Over 25 EndFraction minus ellipsis Sigma-Summation Underscript n = 1 Overscript infinity EndScripts two-thirds (negative 4) Superscript n minus 1 Sigma-Summation Underscript n = 1 Overscript infinity EndScripts (negative 12) (one-fifth) Superscript n minus 1.
Mathematics
1 answer:
Sholpan [36]2 years ago
7 0

The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4.

\sum_{n=1 }^{\infty} \dfrac{2}{3}(-4)^{n-1}

<h3>What is geometric series diverges? </h3>

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

It can be given as,

a+ar+ ar^2+ ar^3+...

Here,

is the (<em>a</em>) first term of the sequence, and (<em>r</em>) is the common ratio.

To be a series as geometric series diverges, it should follow,

|r| > 1

First option given as,

3/5+3/10+3/20+3/40+ ...

Here, the common ratio is,

r=\dfrac{\dfrac{3}{10}}{\dfrac{3}{5}}\\r=\dfrac{1}{2}

The common ratio is less than one. Thus option a is not correct.

First option given as,

-10+4-8/4+18/25- ...

Here, the common ratio is,

r=\dfrac{4}{-10}\\r=\dfrac{-2}{5}

For the option number two the common ratio is (-2/5) which is less than 1. This option is also not correct.

In the option number c, the value of common ratio is -4. The absolute value of common ratio is,

|r|=|-4|\\|r|=4

The absolute value of this common ratio is more than one. Thus, this is the correct option.

The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4.

\sum_{n=1 }^{\infty} \dfrac{2}{3}(-4)^{n-1}

Learn more about the geometric sequence here;

brainly.com/question/1509142

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