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iogann1982 [59]
2 years ago
13

Show that a sequence {sn} coverages to a limit L if and only if the sequence {sn-L} coverages to zero.

Mathematics
1 answer:
Andreyy892 years ago
3 0

Let {s_n}_{n\in\Bbb N} be a sequence that converges to L. This means for any \varepsilon>0, there is some N such that |s_n-L| for all n>N. From this inequality we see that |(s_n-L)-0|, so it follows that s_n-L\to0.

On the other hand, let {s_n-L} be a sequence that converges to 0. This means |(s_n-L)-0| for all large enough n, and we get the simpler inequality for free, |s_n-L|, so it follows that s_n\to L.

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When two dice are rolled, what is the probability the two numbers will have a sum of 5?
ira [324]

When two dice are rolled, then possible outcomes are

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Total possible outcomes = 36

In that, we count the ordered pairs that give us sum 5

(1,4) (2,3) (3,2) and (4,1) = 4 outcomes

Probability = (number of times the event occurs)/ (total number of outcomes)

P( sum of 5) = \frac{4}{36} = \frac{1}{9}

7 0
3 years ago
Can someone please help me? I don't understand this problem. How would they be the same???
musickatia [10]
Area of rectangle = 15 x 8
                           =120

area of parallelogram = 8 x 15 
                               =120
so, they have the same area, because the length of a rectangle is the same as the height of a parallelogram and also for the base.
4 0
3 years ago
The answer is 915 / 7
Naily [24]

Answer:

If you want 915/7 simplified, it is 130.714285714.

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Write an equation perpendicular to x-3y=3 passes through (5,-9)
kherson [118]
3y=x-3
y=1/3x-1
Perpendicular slope: -3
y=-3x+b
Plug in the coordinates in the equation:
-9=-3(5)+b
-9=-15+b
4=b
Equation: y=-3x+4
Also, when finding the perpendicular slope you take the reciprocal of the original slope and make it negative if it is positive and make it positive if it’s negative.
8 0
3 years ago
A company makes 80 bags. 24 of the bags have buttons but no zips. 22 of the bags have zips but no buttons. 29 of the bags have n
Anika [276]
27


Step by step explanation This is how I got the answer to your question and I gave you the solution I hope this helps you out
7 0
2 years ago
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