Answer:
5/6
Step-by-step explanation:
1/2 + 1/4 + 1/12 =
The LCD is 12.
= 6/12 + 3/12 + 1/12
= 10/12
= 5/6
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.
3
+
3
+
3
+
3
+
3
5
5
+
5
+
5
+
5
+
5
+
−
8
+
7
+
7
+
7
+
7
+
7
+
7
+
8
8
+
8
Answer:
Look at the unfolded cylinder down: it's consisted of a rectangle and 2 circles. so to find the surface area of the cylinder we should find the areas of the rectangle and the 2 circles.
1) A of 2 circles = 2(π
) = 2π
2) A of rectangle = base x height (or length x width) = bh
but the if we fold the rectangle? what will happen?
the base will go around the circle, this means that the base is equal to the circle circumference, which is 2πr.
Therefore, A of rectangle = 2πrh
3) Surface area of cylinder = 2π + 2πrh
simplify more and take the common factor 2πr:
= 2πr (r+h)
