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yulyashka [42]
3 years ago
7

Converges or diverges, find the sum. 3 -3/4 +3/16 -3/64.

Mathematics
1 answer:
Gnesinka [82]3 years ago
6 0
We know the terms in this geometric sequence are 3, -3/4, 3/16 and so on.

now.. what's the "r" or common ratio?  well, in a geometric sequence, to get the next term's value you multiply by "r", therefore, if you divide any of those values, by the value before it, the quotient will be, yes, you guessed it, "r".

namely say a, a*b.... now (a*b)/a is just b, the quotient is the value you used as multiplier.

\bf -\cfrac{3}{4}\div 3\implies -\cfrac{3}{4}\div \cfrac{3}{1}\implies -\cfrac{3}{4}\cdot \cfrac{1}{3}\implies -\cfrac{1}{4}

any other two pair of values will spit out the same "r".

now, the Sum of a geometric sequence reaches a limit or point, that is converges, only if the value of "r" is a fraction and more than -1 or less than 1, negative or positive.

or in short, if | r | < 1.

now, in this case, -1/4 is indeed more than -1 and less than 0, therefore, the Sum of the sequence is convergent, it meets at a limit.
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What is the algebraic expressions of 8-6k​
Komok [63]
Eight decreased by six times the number k

The difference of eight and the product of six and the number k

Eight minus six times k

Six multiplied to k is less than 8
4 0
2 years ago
Y=-4x-5 and y=-4x+1<br> Many solitions, one solution, or no solution
GuDViN [60]

There will be no solutions because the lines have the same slope (-4) meaning they are parallel to each other and will not cross.

Hope this helps!!

8 0
3 years ago
Problem 8
SpyIntel [72]
Answer:

Explanation:

1. x represent the copybook while y represent the pen that is bought.

2. 2x + 3y = 9000 means that in order to buy 2 copybooks and 3 pen you have to pay 9000 LL.

3. Solve for the price of x and y

2x + 3y = 9000 (1)
4x + 2y = 8000 (2)

Multiply (1) by -2:

-2(2x + 3y = 9000)
4x + 2y = 8000
——————————
-4x - 6y = -18000
4x + 2y = 8000
—————————
-4y = -10000
y = -10000/-4
y = 2500

Substitute y value into (2):

4x + 2(2500) = 8000
4x + 5000 = 8000
4x = 3000
x = 3000/4
x = 750

Therefore, 1 copy book = 750LL and 1 pen = 2500 LL
3 0
2 years ago
A line passes through point A(10,15). A second point on the line has an x-value that is 125% of the x-value of point A and a y-v
melisa1 [442]

The equation of the line in the point-slope form is y - 15 = -\frac{3}{2} (x - 10)

Step-by-step explanation:

The point-slope form of a linear equation is y-y_{1}=m(x-x_{1}) , where

  • m is the slope of the line, where m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} , (x_{1},y_{1}) and (x_{2},y_{2}) are two points on the line
  • (x_{1},y_{1}) is a point on the line

∵ Point A = (10 , 15)

∵ The x-coordinate of the second point is 125% of x-coordinate

  of point A

∴ x-coordinate of second point = \frac{125}{100} × 10

∴ x-coordinate of second point = 12.5

∵ The y-coordinate of the second point is 75% of y-coordinate

  of point A

∴ y-coordinate of second point = \frac{75}{100} × 15

∴ y-coordinate of second point = 11.25

∴ The coordinates of the second point are (12.5 , 11.25)

Let us find the slope of the line by using the rule of it above

∵ (x_{1},y_{1}) = (10 , 15)

∵ (x_{2},y_{2}) = (12.5 , 11.25)

∴ m=\frac{11.25-15}{12.5-10}=\frac{-3.75}{2.5}=-\frac{3}{2}

Now we can write the equation

∵ The point-slope form is y-y_{1}=m(x-x_{1})

∵ m=-\frac{3}{2}

∵ (x_{1},y_{1}) = (10 , 15)

- Substitute these values in the form of the equation

∴ y - 15 = -\frac{3}{2} (x - 10)

The equation of the line in the point-slope form is y - 15 = -\frac{3}{2} (x - 10)

Learn more:

You can learn more about the linear equation in brainly.com/question/4152194

#LearnwithBrainly

5 0
3 years ago
1 pound is closest in weight to which one of the following Metric units of weight?
timama [110]

Answer:

<h2>4.5 N</h2>

Step-by-step explanation:

To convert 1 pounds to its meteric unit in weight, we need to first convert it to kilogram. Using the conversion 1pound = 0.453592 kg

Since Weight of a substance = mass of the substance * acceleration due to gravity

W = mg

Given mass = 0.453592kg and g = 9.8m/s²

Weight = 4.4452016 Newtons

1 pounds is therefore closest to 4.5 units metric of weight

8 0
3 years ago
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