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Reptile [31]
3 years ago
14

Find the sum of ( 1- 1/n) + (1 - 2/n) + ( 1 - 3/n)...upto n terms

Mathematics
1 answer:
Lapatulllka [165]3 years ago
5 0

Answer:

(n-1) / 2

Step-by-step explanation:

We have that the sum has the form of:

Sn = n / 2 [2 * a + (n-1) * d]

we compute the terms of a and d

a = 1 - 1 / n

a = (n - 1) / n

, that is, the first term, in the case d is the subtraction between the second and the first term, thus:

d = 1 - 2 / n - (1 - 1 / n)

d = 1 - 2 / n - 1 + 1 / n

d = - 1 / n

now if replacing these values:

Sn = n / 2 * [2 * (n - 1) / n + (n-1) * (- 1 / n)

Sn = n / 2 * [2 * (n-1) - (n-1)] / n

Sn = 1/2 * (n-1)

Therefore, the value of that sum is (n-1) / 2

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Uh Expanded form pls? 4.02 x 10^5
Vera_Pavlovna [14]

Answer:

4.02 x 10 x 10 x 10 x 10 x 10

Step-by-step explanation:

The part that needs expanding is the exponent. Since it is to the power of 5 there needs to be 5 written out 10's, all multiplied.

4.02 x 10 x 10 x 10 x 10 x 10

4 0
3 years ago
Read 2 more answers
Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
Katena32 [7]

Answer:

  • A) A = 27.3°, B = 56.1°, C = 96.6°

Step-by-step explanation:

<u>Use the Law of Cosines:</u>

  • A = arccos [(b² + c² - a²)/(2bc)] = arccos [(13.2² + 15.8² - 7.3²)/(2*13.2*15.8)] = 27.3°
  • B = arccos [(a² + c² - b²)/(2ac)] = arccos [(7.3² + 15.8² - 13.2²)/(2*7.3*15.8)] = 56.1°
  • C = 180° - (A + B) = 180° - (27.3° + 56.1°) = 96.6°

Correct choice is A.

3 0
3 years ago
Mario invests 1,500 in a savings account that earns 2% interest a year. He also plans to set aside $50 cash a month. A:2100(1.02
Sedbober [7]

Answer:

<em>1500(1.02)^x  +   600x</em> is how much he has in savings at the end of x years where it be in the bank or elsewhere

Step-by-step explanation:

x is in years

Let's just think about the investment of 1500 in an account earning 2% per year.

Before the years even start, you are at 1500 ( present value).

The next year (year 1), it would be 1500*.02+1500=(1500)(1.02).

The next year (year 2), it would be 1500(1.02)(.02)+1500(1.02)=1500(1.02)(1.02).

We keep multiplying factors of (1.02) each time.

So for year x, you would have saved 1500(1.02)^x.

Now we are saving 50 cash per month. Per year this would be 12(50) since there are 12 months in a year.  12(50)=600.  

So the first year you would have 600.

The second year you would have 600(2) or 1200.

The third year you would have 600(3) or 1800.

Let's put this together:

1500(1.02)^x  +   600x

4 0
3 years ago
Find the perimeter and area of the polygon shown below.
prohojiy [21]

Answer:

I would say it's d (sorry if im wrong)

3 0
2 years ago
What is the area of the yellow triangle?
lesantik [10]

I can't see pictures, but to find the area of a triangle, you multiply the dimensions, as you would a rectangle, but divide the area by 2.

For example, the dimensions of a triangle are 4 and 6.

Multiply the two.

4x6=24.

But don't stop there. Divide 24 by 2.

24/2=12.

So the area of the example triangle is 12.

---

hope it helps

8 0
3 years ago
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