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3 years ago

PLLLLEEEEAAASSSEEE HELP ME I REALLY NEED IT IT'S URGENT!!!!!

Mathematics

1 answer:

krok68 [10]3 years ago

6 0

The answers would be

D
C
A
A

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Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum

const2013 [10]

Answer: The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

$S=\sum_{i=1}^{\infty}15(4)^{i-1}.$

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, $\sum_{i=1}^{\infty}a_i$ is an infinite series, with complex coefficients $a_i$ and we consider the following limit:

$L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.$

Then, the series will be convergent if L < 1 and divergent if L > 1.

For the given series, we have

$a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.$

So, the limit is given by

$L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.$

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

7 0

4 years ago

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Pllllllzzzzzzzzz help me

Fed [463]

Answer:

for the first one he will get $51

the second one is £2.70

Step-by-step explanation:

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3 years ago

What is 437 divided by 10

Scilla [17]

The answer would be 43.7 because 430 divided by 10 is 43 and the extra 7 would be .7

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3 years ago

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What is the radius of a circle if it's diameter is 3m?

Sveta_85 [38]

The radius is half of the diameter so if the diameter is 3 then the radius is 1.5. ANSWER:1.5 what I did was just divide 3by 2 to get half of 3.

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3 years ago

Line i and line h intersect at what point

Svet_ta [14]

Step-by-step explanation: The intersection of two figures can

be defined as the set of points that is contained in both figures.

In this figure, lines h and i intersect at C or we can

say that C is the intersection of lines h and i.

In this figure, C is the intersection of lines h and i

because C is the point contained by both h and i.

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3 years ago