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Ksenya-84 [330]
3 years ago
7

Calculate the sum of the first 50 terms in the sequence

Mathematics
1 answer:
Anestetic [448]3 years ago
8 0

Answer:

90

Step-by-step explanation:

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Can someone plz help me on this thank you sooo much
Stells [14]

Answer:

the last answer

Step-by-step explanation:

6 0
2 years ago
If n is a positive integer, how many 5-tuples of integers from 1 through n can be formed in which the elements of the 5-tuple ar
Oksana_A [137]

Answer:

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

Step-by-step explanation:

Lets divide it in cases, then sum everything

Case (1): All 5 numbers are different

 In this case, the problem is reduced to count the number of subsets of cardinality 5 from a set of cardinality n. The order doesnt matter because once we have two different sets, we can order them descendently, and we obtain two different 5-tuples in decreasing order.

The total cardinality of this case therefore is the Combinatorial number of n with 5, in other words, the total amount of possibilities to pick 5 elements from a set of n.

{n \choose 5 } = \frac{n!}{5!(n-5)!}

Case (2): 4 numbers are different

We start this case similarly to the previous one, we count how many subsets of 4 elements we can form from a set of n elements. The answer is the combinatorial number of n with 4 {n \choose 4} .

We still have to localize the other element, that forcibly, is one of the four chosen. Therefore, the total amount of possibilities for this case is multiplied by those 4 options.

The total cardinality of this case is 4 * {n \choose 4} .

Case (3): 3 numbers are different

As we did before, we pick 3 elements from a set of n. The amount of possibilities is {n \choose 3} .

Then, we need to define the other 2 numbers. They can be the same number, in which case we have 3 possibilities, or they can be 2 different ones, in which case we have {3 \choose 2 } = 3  possibilities. Therefore, we have a total of 6 possibilities to define the other 2 numbers. That multiplies by 6 the total of cases for this part, giving a total of 6 * {n \choose 3}

Case (4): 2 numbers are different

We pick 2 numbers from a set of n, with a total of {n \choose 2}  possibilities. We have 4 options to define the other 3 numbers, they can all three of them be equal to the biggest number, there can be 2 equal to the biggest number and 1 to the smallest one, there can be 1 equal to the biggest number and 2 to the smallest one, and they can all three of them be equal to the smallest number.

The total amount of possibilities for this case is

4 * {n \choose 2}

Case (5): All numbers are the same

This is easy, he have as many possibilities as numbers the set has. In other words, n

Conclussion

By summing over all 5 cases, the total amount of possibilities to form 5-tuples of integers from 1 through n is

n + 4 {n \choose 2} + 6 {n \choose 3} + 4 {n \choose 4} + {n \choose 5}

I hope that works for you!

4 0
3 years ago
The children's section is rectangular and has three of its corners at (-10, 10), (-10, 4), and (-3, 10). What is the area of the
Veronika [31]

Answer:

I don't know the answer, sorry! But I'm stuck on this question too and I was wondering if you figured out the answer?

Step-by-step explanation:

8 0
3 years ago
A children's inflatable pool takes 22 minutes to fill with an electric air pump. It takes 50 minutes to let the air out of the p
WARRIOR [948]
Im assuming it has the same amount of air pressure so it wold take roughly  double the time. So I would say 44 minutes.
6 0
3 years ago
What is the slope of the line?
Simora [160]

Answer:

The slope is 0.5 or (1/2)

Step-by-step explanation:

Find the rise over run.

from -3 to -1 and 2 to 3 rises 1 runs 2 so then you divide 1/2 and get 0.5.

8 0
3 years ago
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