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Blizzard [7]
2 years ago
12

Does the following series converge or diverge?

Mathematics
1 answer:
Alex777 [14]2 years ago
7 0

Answer:

converge

Step-by-step explanation:

the reason is : the individual terms of the series get smaller and smaller towards 0, and therefore the sum converges to a certain limit.

why do I know that the individual terms get smaller and smaller ?

because the terms are ultimately (with n getting very large the constant factors added constants become irrelevant)

n / (n^(3/2))

as sqrt(n³) = n^(3/2)

and n^(3/2) progresses much faster and stronger than n (or n¹), as 3/2 is larger than 1.

so, the denominator (bottom) of that fraction grows stronger than the numerator (top), and the terms go therefore against 0 with larger and larger n.

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Find (r-s) (t-s) + (s-r) (s-t) for all numbers r, s, and t. (a) 0 (b) 2 (c) 2rt (d) 2(s-r) (t-s) (e) 2(r-s) (t-s)
lyudmila [28]
Notice that the 2 expressions have 2 common terms.

(r-s) is just (s-r) times (-1)

similarly

(t-s) is just (s-t) times (-1)

this means that :

(r-s) (t-s) + (s-r) (s-t)=-(s-r)[-(s-t)]+(s-r) (s-t)

the 2 minuses in the first multiplication cancel each other so we have:

-(s-r)[-(s-t)]+(s-r) (s-t)=(s-r) (s-t)+(s-r) (s-t)=2(s-r) (s-t)

Answer:

d)<span>2(s-r) (t-s) </span>
3 0
4 years ago
Read 2 more answers
Solve for t:<br><br> t + 1 = 24<br> A. t = 23<br> B. t = 25<br> C. t = 31<br> D. t = 20
Flauer [41]

Answer:

t = 25

Step-by-step explanation:

T is 25 because you take 1 away from the t+1 side and add the 1 to the 24 side.

3 0
3 years ago
Read 2 more answers
When you multiply a function by -1 what is the effect on its graph?
vlada-n [284]

Answer:

Step-by-step explanation:

Depends on what you mean by multiplying by - 1.  I assume you are not going to multiply the y or f(x) term by - 1.

If that is so, take an example. Suppose you have a graph that is y=x^2

That's a parabola that opens upwards and it has a line going through its focus which is a point on the +y axis.

When you multiply the right hand side by - 1, the graph you get will be y = - x^2.

That opens downward and the focus is on the - y axis.

That means that the effect of the graph is that it flips over the x axis, which I think is the third answer.

5 0
3 years ago
Please help!! Question is above in the image
klasskru [66]

9514 1404 393

Answer:

  $503.85

Step-by-step explanation:

The amortization formula can help with this.

  A = P(r/12)/(1 -(1 +r/12)^(-n))

where P is the loan value, A is the monthly payment, r is the annual interest rate, and n is the number of monthly payments.

We want to find P. All of the other values are given.

  P = A(1 -(1 +r/12)^-n)/(r/12)

  P = 32.48(1 -1.012667^-18)/(0.012667) = 31.48·16.0054

  P ≈ 503.85

The equivalent cash price is about $503.85.

7 0
3 years ago
1
ss7ja [257]

Answer:

32.08488741

Step-by-step explanation:

4 0
3 years ago
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