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3 years ago

Find the sum of the following infinite geometric series, if it exists.

Mathematics

2 answers:

zvonat [6]3 years ago

7 0

Answer: Does not exist

Step-by-step explanation:

The given geometric series : $60 + 84 + 117.6 + 164.64 +…$

Here the first term : $a=60$

The second term : $ar=84$

Now, the common ratio in this series will be :_

$r=\dfrac{ar}{a}=\dfrac{84}{60}=1.4>1$

We know that if the common ratio in infinite geometric series does not lies between (-1,1) , then the series is diverging. And the sum of the infinite geometric series will not exists.

Hence, the sum of the given infinite geometric series does not exist.

Rasek [7]3 years ago

4 0

$q=\dfrac{84}{60}=1.4 > 1\ \text{ therefore you answer: Does not exist}$

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Alexeev081 [22]

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cricket20 [7]

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Step-by-step explanation:

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divide by -5

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3 years ago

Read 2 more answers

Point m is the midpoint of kL. M(1,-1) and L(8,-7. What are the coordinates of point k?

Phoenix [80]

Answer: (-6, 5)

<u>Step-by-step explanation:</u>

Use the Midpoint Formula: $\dfrac{(x_k, y_k)+(x_L,y_L)}{2}=(x_m, y_m)$

Separate the x's and y's and solve them individually:

$\dfrac{x_k+x_L}{2}=x_m\qquad \qquad \qquad \qquad\dfrac{y_k+y_L}{2}=y_m\\\\\\\dfrac{x_k+8}{2}=1\qquad \qquad \qquad \qquad \qquad \dfrac{y_k-7}{2}=-1\\\\\\x_k+8=2\qquad \qquad \qquad \qquad \qquad y_k-7=-2\\\\\\x_k\quad =-6 \qquad \qquad \qquad \qquad \qquad y_k\qquad =5$

So, the k-coordinate is (-6, 5)

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