Answer:
- (a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers.
- (b) A series is divergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent.
Step-by-step explanation:
A sequence is a list of ordered numbers. For example, 1, 2, 3, 4, 5.... is a sequence. The numbers are listed in a specific order when we count. In contrast, a series is the sum of the numbers in a sequence. For this multiple choice, choose the best answer that defines what a sequence is.
(a) What is the difference between a sequence and a series?
- A series is an unordered list of numbers whereas a sequence is the sum of a list of numbers.
- A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers.
- A series is an ordered list of numbers whereas a sequence is the sum of a list of numbers.
- A sequence is an ordered list of numbers whereas a series is an unordered list of numbers.
- A sequence is an unordered list of numbers whereas a series is the sum of a list of numbers.
When working with sequences and series, we look at what happens at negative and positive infinity. When a series converges, it approaches a finite number. When a series diverges, it does not approach a finite number but infinity.
(b) What is a convergent series? What is a divergent series?
- A series is divergent if the nth term converges to zero. A series is convergent if it is not divergent.
- A series is convergent if the nth term converges to zero. A series is divergent if it is not convergent.
- A convergent series is a series for which lim n → ∞ an exists. A series is convergent if it is not divergent.
- A series is convergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent.
- A series is divergent if the sequence of partial sums is a convergent sequence. A series is divergent if it is not convergent.
Answer:
four angles at point B in this second diagram.
Step-by-step explanation:
<h3>
Answer: Choice B) real and integer</h3>
Explanation:
The set of integers is {..., -3, -2, -1, 0, 1, 2, 3, ...} basically its the set of positive and negative whole numbers, including 0 as well. The set of whole numbers is {0, 1, 2, 3, 4, ...} so any positive number that does not a fractional or decimal part. The value 0 is included in the set of whole numbers. The natural numbers is {1, 2, 3, 4, ...} so it is the set of whole numbers but we kicked out 0 from this set. The set of natural numbers is also called the set of counting numbers.
If we take any two integers and divide them then you'll get a rational number. You cannot have zero in the denominator, but you can have any other integer. For example, 2 and 3 divide to get the fraction 2/3 which is a rational number. Numbers that we cannot express as a fraction of two integers are said to be irrational. An example of this is pi = 3.14 which is irrational. We cannot write pi as a ratio of two integers. One approximation is pi = 22/7, but this doesn't represent pi exactly. Any integer itself is rational. Something like -13 can be written as -13/1, so we cannot say -13 is irrational. That rules out choice A. Choice C is ruled out because negative numbers aren't natural numbers. The same can be said about -13 not being part of the whole number set {0, 1, 2, 3, 4, ...} so choice D is also false.
Answer:
the answer is 3x2-10x+6=0
Answer:
7.8 cm and 25.3 cm
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
?² + 7² = 10.5²
?² + 49 = 110.25 ( subtract 49 from both sides )
?² = 61.25 ( take the square root of both sides )
? = 
≈ 7.8 cm ( to 1 dec. place )
Then
P = 10.5 + 7 + 7.8 = 25.3 cm
