3 years ago

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Mathematics

1 answer:

snow_tiger [21]3 years ago

6 0

C I think I’m not sure

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The sum of an infinite geometric series is three times the first term. Find the common ratio of this series.

adelina 88 [10]

Answer:

$\frac{2}{3}$

Step-by-step explanation:

The sum of an infinite geometric series is expressed according to the formula;

$S_\infty = \dfrac{a}{1-r}$ where;

a is the first term of the series

r is the common ratio

If the sum of an infinite geometric series is three times the first term, this is expressed as $S_\infty = 3a$

Substitute $S_\infty = 3a$ into the formula above to get the common ratio r;

$3a = \dfrac{a}{1-r} \\\\$

$cross \ multiply\\\\3a(1-r) = a\\\\3(1-r) = 1\\$

open the parenthesis

$3 - 3r = 1\\\\$

subtract 3 from both sides

$3 - 3r -3= 1-3\\\\-3r = -2\\\\r = \frac{2}{3}$

Hence the common ratio of this series is $\frac{2}{3}$

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The Explanation: You need to uses distributive property to 6x to x^2+3 which will be 6x^3+18x

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