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alexgriva [62]
3 years ago
6

Evaluate the geometric series or state that it diverges. one ninth 1 9plus+startfraction 7 over 81 endfraction 7 81plus+startfra

ction 49 over 729 endfraction 49 729plus+startfraction 343 over 6561 endfraction 343 6561plus+...
Mathematics
2 answers:
olasank [31]3 years ago
6 0
The series converges, and its sum is 1/2.

If r > 1, the series is divergent.  If r < 1, the series is convergent.  In our sequence, r, the common ratio we multiply by to get the next term, is 7/9; therefore it is convergent.

To find the sum of a convergent series, we use the formula
a/(1-r), where a is the first term and r is the common ratio.  We then have
1/9÷(1-7/9) = 1/9÷2/9 = 1/9×9/2 = 1/2
abruzzese [7]3 years ago
5 0

Answer:

In the given geometric series, r, the common ratio is 7/9; therefore the series is convergent.  

Step-by-step explanation:

We are given the geometric series:

\frac{1}{9} + \frac{7}{81} + \frac{49}{729} + \frac{343}{6561} + ...

The general geometric series is in the for a, ar, ar^2, ar^3, ..., where a is the first term and r is the common ratio.

Comparing with the given geometric series, we have, a = \frac{1}{9} \text{ and }r = \frac{7}{9}

If r > 1, the series is divergent.  

If r < 1, the series is convergent.

In the given geometric series, r, the common ratio is 7/9; therefore the series is convergent.

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Help me on the first question pls
Margaret [11]
To do the first question, simplify the equation, putting like terms together, by adding and subtracting to do this.

Then looking at the equation that you solved for, look and see if there are any other equations that are related in some way to the original solved equation.

Pay close attention to the positive and negative signs.






3 0
3 years ago
A textbook store sold a combined total of 290 math and history textbooks in a week. The number of math textbooks sold was 64 mor
11Alexandr11 [23.1K]

Answer:

113

Step-by-step explanation:

290 - 64 = 226

226 ÷ 2 = 113

4 0
2 years ago
Consider the numbers 4/15 and 3/10 (a) Compare the numbers. (B) find a fraction between the two given numbers
valentinak56 [21]
As a decimal 4/15 = 0.2666667
As a decimal 3/10 = 0.3 [talk about close]
3/10 is bigger.

You could take an average to find something between 4/15 and 3/10
1/2(4/15 + 2/10)
1/2(8/30 + 6/30)
1/2(14/30)
1/2(7/15)
7/30 is between the two given numbers..
5 0
3 years ago
What is the y intercept for y = -4x + 19 y = 2x + 1
max2010maxim [7]

y=mx+b\\\\m-slope\\b-y\ intercept\\\\y=-4x+\boxed{19}\to\ y\ intercept\ is\ 19\to(0;\ 19)\\\\y=2x+\boxed{1}\to\ y\ intercept\ is\ 1\to(0;\ 1)

4 0
3 years ago
Tommy ate 512 of pizza, Johnny ate 14 of the pizza, and Mike ate 112 of the same pizza. How much of the pizza did they eat toget
statuscvo [17]

Answer:

126

Step-by-step explanation:

112 plus 14 equals to 126

they ate 126 pizzas all together

5 0
3 years ago
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