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xxMikexx [17]
2 years ago
15

Match each series with the equivalent series written in sigma notation

Mathematics
1 answer:
PIT_PIT [208]2 years ago
5 0

Answer:

3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n

4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n

2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n

3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n

Step-by-step explanation:

Given

See attachment for complete question

Required

Match equivalent expressions

Solving (a):

3 + 12 + 48 + 192 + 768

The expression can be written as:

3 \to 3*4^{0 --- 0

12 \to 3 * 4^{1 ---- 1

48 \to 3 * 4^{2 --- 2

192 \to 3 * 4^{3 ---- 3

768 \to 3 * 4^{4 ---- 4

For the nth term, the expression is:

Term = 3 * 4^{n ---- n

So, the summation is:

3 + 12 + 48 + 192 + 768 = \sum\limits^4_{n=0} 3 * 4^n

Solving (b):

4 + 32 + 256 + 2048 + 16384

The expression can be written as:

4 \to 4 * 8^0 --- 0

32 \to 4 * 8^1 ---- 1

256 \to 4 * 8^2 --- 2

2048 \to 4 * 8^3 ---- 3

16384 \to 4 * 8^4 ---- 4

For the nth term, the expression is:

Term \to 4 * 8^n ---- n

So, the summation is:

4 + 32 + 256 + 2048 + 16384 = \sum\limits^4_{n=0} 4 * 8^n

Solving (c):

2 + 6 + 18 + 54 + 162

The expression can be written as:

2 \to 2 * 3^0 --- 0

6 \to 2 * 3^1 ---- 1

18 \to 2 * 3^2 --- 2

54 \to 2 * 3^3 ---- 3

162 \to 2 * 3^4 ---- 4

For the nth term, the expression is:

Term \to 2 * 3^n ---- n

So, the summation is:

2 + 6 + 18 + 54 + 162 = \sum\limits^4_{n=0} 2* 3^n

Solving (d):

3 + 15 + 75 + 375 + 1875

The expression can be written as:

3 \to 3 * 5^0 --- 0

15 \to 3 * 5^1 ---- 1

75 \to 3 * 5^2 --- 2

375 \to 3 * 5^3 ---- 3

1875 \to 3 * 5^4 ---- 4

For the nth term, the expression is:

Term \to 3 * 5^n ---- n

So, the summation is:

3 + 15 + 75 + 375 + 1875 = \sum\limits^4_{n=0} 3* 5^n

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Which shaded region? are you talking about the region between the circle and square?
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3 years ago
What value, entered in the blank below, would make the two expressions equivalent? Expres
malfutka [58]

Answer:

The value is -3

Step-by-step explanation:

Here in this question, we are interested in making the expressions on both sides of the equation equal. But we seek a particular value or number which when placed in front of the quadratic expression on the right hand side makes the equations equal.

To get this done with, we will need to factorize the expression on the left hand side of the equation.

Thus, we can write;

-27x^2 + 9x + 12 as 3(-9x^2 + 3x + 4)

What do we notice? we can see that the now factored quadratic expression resembles what we have on the right hand side asides there fact that we are not there yet in terms of sign.

Thus, we can finally write ;

-27x^2 + 9x + 12 as -3(9x^2 -3x -4)

This exactly gives the expression on the right hand side

Thus the value to place in the blank is -3

5 0
3 years ago
Planet X has a mass of 8.46 x 1022 kg. Planet Y has a mass of 5,028,000,000,000,000,000,000,000 kilograms. How many times the ma
kramer

Answer:

59.4 times greater to the nearest tenth.

Step-by-step explanation:

5,028,000,000,000,000,000,000,000

= 5.028 * 10^24

So the required ratio =  5.028 * 10^24 / 8.46 * 10^22

= 0.594326 * 10^2

= 5.94326 * 10

= 59.4326.

4 0
3 years ago
PLEASE HELP IM DESPERATE WILL GIVE BRAINLIEST ONLY ANSWER IF YOU ARE HELPING
VARVARA [1.3K]

Answer:

48

Step-by-step explanation:

u • w

= (i + 6j ) • (9i - 2j )

= (1 × 9 ) + (6 × - 2 )

= 9 + (- 12)

= 9 - 12

= - 3

v • w

= (5i - 3j ) • (9i - 2j )

= (5 × 9) + (- 3 × - 2)

= 45 + 6

= 51

Then

u • w + v • w

= - 3 + 51

= 48

7 0
3 years ago
Identify the error by providing a brief description. Then, complete the problem correct
Ipatiy [6.2K]

Answer:

True answer: -24

Step-by-step explanation:

<em><u>Showing the error</u></em>

-16-2(-2) – 12   First you need to multiply

8(-2) - 12   The error here is that the wrong numbers are multiplied together

-16-12    Add the negatives together

-28​  Your answer (the incorrect one)

<em><u /></em>

<em><u>The correct way of solving it</u></em>

-16 -2(-2) - 12  Multiply into the parenthesis

-16 + 4 -12   Add the first two numbers

-12 - 12  Add the numbers together

-24  The answer

8 0
3 years ago
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