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BlackZzzverrR [31]
2 years ago
12

Order the numbers from least to greatest. 0.3, 9/25, 33%, 0.35

Mathematics
1 answer:
Finger [1]2 years ago
5 0

Answer:

0.3(least)

0.33

0.35

0.36(greatest)

Step-by-step explanation:

Okay, so first we need to have all of our numbers in the same category of variable. So first, we will convert 9/25 to a decimal.

To do that, we must divide 9 by 25 to get our answer of 0.36.

Now, we will convert the 33% to a decimal by dividing it by 100 to get 0.33

We now have our list, which should be ordered as:

0.3

0.33

0.35

0.36

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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}.

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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.

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