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kozerog [31]
2 years ago
5

What is the sum of the infinite geometric series 9−6+4−83+...9-6+4-83+...??

Mathematics
1 answer:
vivado [14]2 years ago
7 0
Successive terms have a common factor of -\dfrac23, which means the nth partial sum of the series can be written as

S_n=9-6+4-\dfrac83+\cdots+9\left(-\dfrac23\right)^{n-1}
S_n=9\left(1+\left(-\dfrac23\right)^1+\left(-\dfrac23\right)^2+\left(-\dfrac23\right)^3+\cdots+\left(-\dfrac23\right)^{n-1}

\implies-\dfrac23S_n=9\left(\left(-\dfrac23\right)^1+\left(-\dfrac23\right)^2+\left(-\dfrac23\right)^3+\left(-\dfrac23\right)^4+\cdots+\left(-\dfrac23\right)^n\right)

\implies S_n-\left(-\dfrac23\right)S_n=9\left(1-\left(-\dfrac23\right)^n\right)
\dfrac53S_n=9\left(1-\left(-\dfrac23\right)^n\right)
S_n=\dfrac{27}5\left(1-\left(-\dfrac23\right)^n\right)

As n\to\infty, the geometric term vanishes, leaving you with

S=\displaystyle\lim_{n\to\infty}S_n=\dfrac{27}5
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Answer:

Maybe f(a) = 0.5b?

But it's not in terms of a.

Step-by-step explanation:

Simplify the equation:

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2 years ago
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Ugo [173]

Answer:

-1/6 and 1 1/6

I included an image showing the points to select, in red and the point we start at, in blue.

Step-by-step explanation:

We need to get the numbers they tell us (2/3 & 1/2) to have the same denominators as the numbers on the number line before we can start.

1/2 is just the simplified form of 3/6 and 2/3 is just the simplified form of 4/6.

So 1/2 is actually 3/6 on the number line.

Now we need to find the numbers that are 2/3 (or 4/6) unit away from 3/6.

Count 4 units to the right and 4 to the left of 3/6 to get the numbers we are looking for.

These numbers are -1/6 and 1 1/6

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Pic is attached below.


5 0
3 years ago
What is -2.25 + (-3.75)
barxatty [35]

Answer:−6

Step-by-step explanation:

−2.25−3.75

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6 0
3 years ago
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natima [27]
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4 0
3 years ago
What is the missing length??
amid [387]

Answer

The missing length is 10

Step-by-step explanation:

Represent the missing length with x

The sides of the given shape are directly proportional.

Mathematically:

(15 + x) to (12 + 8) and x to 7

Represent as a ratio:

(15 + x) : (12 + 8) = x : 8

15 + x : 20= x : 8

Convert to fraction

\frac{15 + x}{20} = \frac{x}{8}

Cross Multiply:

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120 + 8x = 20x

Collect Like Terms

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12x = 120

Solve for x

x = \frac{120}{10}

x = 10

<em>The length of the missing side is 10</em>

4 0
3 years ago
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