Find a formula for the nth partial sum Sn of the following series. If the series is finite, determine the sum. If the series is
infinite, determine if it converges or diverges, and if it converges, determine the sum. Please simplify your solution.
1 answer:
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Answer:
156
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right<u> </u>
<u>Algebra I</u>
- Functions
- Function Notation
- Average Rate of Change:
Step-by-step explanation:
<u>Step 1; Define</u>
<em>Identify</em>
f(x) = 5ˣ + 1
Interval <em>x</em> [0, 4] →<em>b</em> = 4, <em>a</em> = 0
<u>Step 2: Find Rate of Change</u>
- Substitute in variables [Average Rate of Change]:
- [Average Rate of Change] Substitute in <em>x</em> [Function f(x)]:
- (Parenthesis) Evaluate exponents:
- (Parenthesis) Add:
- [Fraction] Subtract:
- Divide:
The attached file is the points graphed.
So what is a linear function?
<span>If it is a linear function, its graph will be a straight line.
</span><span>It also must have either one or two variables. If there is another variable is, it must be a known variable or constant.
</span>
The points and the graph satisfy both of these things, so we know the answer is not B or D.
So, let's look at both answer choices.
<span>
A.It is a linear function because the input values are increasing.
C.</span><span>It is a linear function because there is a constant rate of change in both the input and output.
Well, according to our criteria, the input values don't need to be increasing for it to be linear. But, we do know that there must be a constant rate of change in both the input and output.
So, the answer is C. </span>It is a linear function because there is a constant rate of change in both the input and output.<span>
</span>
So what is a linear function?
<span>If it is a linear function, its graph will be a straight line.
</span><span>It also must have either one or two variables. If there is another variable is, it must be a known variable or constant.
</span>
The points and the graph satisfy both of these things, so we know the answer is not B or D.
So, let's look at both answer choices.
<span>
A.It is a linear function because the input values are increasing.
C.</span><span>It is a linear function because there is a constant rate of change in both the input and output.
Well, according to our criteria, the input values don't need to be increasing for it to be linear. But, we do know that there must be a constant rate of change in both the input and output.
So, the answer is C. </span>It is a linear function because there is a constant rate of change in both the input and output.<span>
</span>