1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
iogann1982 [59]
3 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:
Andreyy893 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.

You might be interested in
Which linear function represents the line given by the point-slope equation y – 8 = (x – 4)? f(x) = x + 4 f(x) = x + 6 f(x) = x
andrew11 [14]
It is understood without being written that the slope of this line is 1.  If we rewrite the point-slope form of the line it would be y-8=1(x-4) where 1 is the slope.  We move the -8 over by addition to get y = 1x-4+8, or, simplified, y=x+4, the first choice in your answers.
7 0
3 years ago
Read 2 more answers
Which is the best description for this graph? <br> Someone Please help me :)
wlad13 [49]
The answer would be the second one, the graph is decreasing everywhere
4 0
3 years ago
Read 2 more answers
The width of a room is 60% of the land is 10 feet what is the area of the room
nikdorinn [45]
I believe it is 600.

8 0
3 years ago
What is the inverse function f(x)=1/4x-2
Cloud [144]

The inverse function of the function above is f(x) = 4x + 8

You can find the inverse to any function by switching the x and f(x) values. After that, solve for the new f(x) value. The result will be the inverse function. The step-by-step process for this one is done below for you.

f(x) = 1/4x - 2 ----> Start by switching the f(x) and x

x = 1/4f(x) - 2 ----> Now add 2 to both sides

x + 2 = 1/4f(x) ----> Now multiply both sides by 4

f(x) = 4x + 8

Now that you've solved it for the new f(x), you have your inverse function.

3 0
3 years ago
Without calculating, is the equation (1.8 times 3) times 2.1 = ( 1.8 times 2.1 ) true or false? Explain your reasoning.
Paladinen [302]
It is true due to the commutative property of multiplication. If all of your operations are multiplication, then the integers can move around and you can still get the same answer. 
^This is only true if you meant to type (1.8x3)x2.1=(1.8x2.1)x3

If you meant what you typed, then the equation is false. The left side would be 3 times the value of the right side due to the 3 being on the left side and not the right side while without the 3 the two sides would be equal.
6 0
3 years ago
Other questions:
  • Megan invested in ten bonds of total face value of $1.000, issued by Zen Corporation. The bonds paid 10 percer semiannual (5% ev
    9·1 answer
  • What is the answer to this?
    12·1 answer
  • In which of the number lines does the plotted point represent a number greater than -1 1/2? Check all that apply.
    5·2 answers
  • Write an equation for the transformation of y = x.
    14·1 answer
  • Describe a situation that models a nonlinear pattern.
    9·1 answer
  • Given a+b=7 and a–b=3, find: 2a·2b
    8·1 answer
  • 3,15,75,375 9th term
    12·1 answer
  • LIST THE ANGLES OF THE TRIANGLE FROM LEAST TO GREATEST ILL BRAINLIEST YOU IF YOU GET IT RIGHT
    14·1 answer
  • Simplify each expression<br> 2) 4 ( 3p-8 ) + 7p
    15·2 answers
  • The smith family bill at a restaurant is $56.00 how much money should mrs snitch leave as a tip if she plans to tip %15
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!