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boomerjm
30.08.2019 •
Mathematics
Give the definition of sequence of real numbers (xn). then give 2 example.
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Ответ:
First I give you an intuitive idea of sequence of real numbers. You can think it as an infinite list of real numbers, so you have that two such infinite lists are equal if and only if their first numbers coincide, their second numbers coincide, their third numbers coincide, and so on. Observe that if we change the position of the numbers we could obtain another infinite list.
This is the precise definition: A sequence of real numbers is a function
. Where
and
are natural and real numbers respectively.
Note that I called the function
for convenience; for the next reason. Usually we write
instead of
for the value at
of the function
.
So if we think the function
as a list, we have that its first number is
(or
if we admite
), its second number is
, and so on.
For the examples you can give an algebraicaly manner to obtain the terms of the sequence (the values of the function
). So for example the sequence
is given by the formula
Or for example a more complicated sequence given by de formula
.
Ответ:
In properties of exponents, if the exponent is negative then you move the variable with the negative exponent to the denominators place and it changes to positive and the numerator becomes 1.
p^-4=1/(p^4)
Also, if no exponent is present it is understood to be 1.
Keeping this in mind,
p^-4 x -5p
1/(p^4) x -5p^1 substituted p^-4 by 1/p^4 and added ^1 to -5p
-5p^1/p^4 multiplied-5p^1 to 1
-5/p^3 simplified