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larisa86 [58]
2 years ago
6

Consider the following series.

Mathematics
1 answer:
Tems11 [23]2 years ago
5 0

Answer:

The series is convergent.

Step-by-step explanation:

1/4 + 1/8 + 1+12 + 1/16 + 1/20

In each term, the numerator stays 1, while the denominator is multiplied by 4. Thus, the series is given by:

\sum_{n=1}^{\infty} \frac{1}{4n}

Convergence test:

We compare the sequence of this test, f_n = \frac{1}{4n}, with a sequence g_n = \frac{1}{n}.

If \lim_{n \rightarrow \infty} \frac{f_n}{g_n} \neq 0, the series is convergent. So

\lim_{n \rightarrow \infty} \frac{f_n}{g_n} = \lim_{n \rightarrow \infty} \frac{\frac{1}{4n}}{\frac{1}{n}} =  \lim_{n \rightarrow \infty} \frac{n}{4n} = \lim_{n \rightarrow \infty} \frac{1}{4} = \frac{1}{4} \neq 0

As the limit is different of zero, the series is convergent.

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3 years ago
A container is shaped like a triangle prism. Each base of container is an equilateral triangle with the dimensions shown. The co
Aleks04 [339]

Answer:

\text{Lateral surface area of container}=270\text{ cm}^2    

Step-by-step explanation:

Please find the attachment.

We have been given that a container is shaped like a triangle prism. Each base of container is an equilateral triangle with each side 6 cm. The height of container is 15 cm.

To find the lateral surface area of our given container we will use lateral surface area formula of triangular prism.

\text{Lateral surface area of triangular prism}=(a+b+c)*h, where, a, b and c represent base sides of prism and h represents height of the prism.

Upon substituting our given values in above formula we will get,

\text{Lateral surface area of container}=(\text{6 cm+ 6 cm+6 cm})*\text{15 cm}

\text{Lateral surface area of container}=\text{18 cm}*\text{15 cm}

\text{Lateral surface area of container}=270\text{ cm}^2

Therefore, lateral surface area of our given container is 270 square cm.

6 0
3 years ago
What is the value of x?
kotegsom [21]

Answer:

X=15

Step-by-step explanation:

A +B + C = 180

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X= 15

4 0
3 years ago
Nolan correctly spelled 13/16 of his spelling words how is 13/16 written as a decimal
ivolga24 [154]

Answer:

0.8125

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
PLS HELP I WILL GIVE THE BRAINLIEST ANSWER
seropon [69]

Answer:

6

Step-by-step explanation:

If V = IR, then V = 40 * 3 in this case, which means V = 120. Quote question, "Assume voltage remains constant." This means V still equals 120 in the second scenario, which we can input into I = V / R to make I = 120 / 20 = 6.

Hope this helps!

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3 years ago
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