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Romashka [77]
2 years ago
5

Determine whether the geometric series is convergent or divergent. If it is convergent, find its sum. (If the quantity diverges,

enter DIVERGES.) 9 + 8 + 64 9 + 512 81 +
Mathematics
1 answer:
pogonyaev2 years ago
4 0

The given geometric series is convergent and the sum of this series is 81.

According to the statement

we have given that the geometric series and we have to find that the convergent or divergent and If it is convergent, find its sum.

So, For this purpose, we know that the

The given geometric series is

9 + 8 + 64/9 + 512/81 + .....

And the common ratio from this G.P. series

r = term 2 / term 1 = 8/9

So, r = 8/9

8/9 < 1

so This series is convergent.

And now the sum of series is according to the summation formula:

Sum = 9/(1 - 8/9)

Sum = 9/(1/9)

Sum = 81.

So, The given geometric series is convergent and the sum of this series is 81.

Learn more about Geometric series here

brainly.com/question/24643676

#SPJ4

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For any positive number b not equal to 1 and any number or variable n, evaluate the following expression.
kirza4 [7]

Answer:

 log_{b} b^{n} = n.

Step-by-step explanation:

Given :  log_{b} b^{n} , b is any positive number not equal to 1 and n is any number.

To find : Evaluate the expression  log_{b} b^{n}.

Formula used : log_{b} x^{y}. = y ∙ log_{b}(x) and

log_{b}(b) = 1.Solution : We have  [tex]log_{b} b^{n}.

By logarithm rule :  log_{b} x^{y}. = y ∙ log_{b}(x).

Then  log_{b} b^{n} = n∙ log_{b}(b).

By logarithm rule :  log_{b}(b) = 1.Now, n∙ [tex]log_{b}(b) = n.

Therefore,  log_{b} b^{n} = n.

5 0
3 years ago
Read 2 more answers
A Formula 1 racing car has a top speed of 350 km/h.
netineya [11]

Answer: f1 car

Step-by-step explanation:

3 0
3 years ago
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What is the slope of the line?<br> y+1=3(x-4)y+1=3(x−4)
sergeinik [125]

Answer:

3

Step-by-step explanation:

y+1=3(x+4)

it is of the form

y-y1=m(x-x1)

where m is the slope

so slope=3

3 0
4 years ago
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Please help <br><br> Evaluate 6 to the power of 2 divided (3 + 9).
Vikki [24]

Answer:

3.272727

Step-by-step explanation:

6^2/(3+9)

= 6^2/(11)

= 36/(11)

= 3.272727

5 0
3 years ago
1
Alona [7]

The speed of current will be "4.5 mph" and the rate Pratap can row in still water will be "8.5 mph".

What does "speed" mean in mathematics?

  • Speed is what it means. the speed of a change in an object's location in any direction.
  • Speed is defined as the ratio of distance to the amount of time it took to cover that distance.
  • Speed is a scalar quantity because it just has a direction and no magnitude.

Given:

Distance "26 miles" in time "2 hours".

Let,

Speed of water = y

Pratap speed when rowing in still water = x

As we know,

      Speed = distance/time

then,

  x + y = 26/2

  x + y = 13

 x = 13 - y

In return trip took him time "6.5 hours",

       x - y = 26/6.5

      x - y = 4

By substituting the value of "x", we get

 13 - y - y = 4

  13 - 2y = 4

     2y = 13 - 4

        2y = 9

          y = 9/4 = 4.5 mph (Rate of the current)

By substituting the value of "y", we get

    x = 13 - a

   x = 13 - 4. 5 = 8.5 mph (Pratap can row in still water)

Learn more about speed

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4 0
2 years ago
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