How to find the nth term of this Series.

In summary, the conversation is about calculating the Taylor polynomial of degree 4 for f(x)=sin(3x) and finding the 156th term of the infinite Taylor Series for g(x)=sin(3x). The person is seeking clarification on how to use the nth term for infinite series equation on the polynomial they have developed and if it is asking for something different. They are also asked to look at the pattern of the formulas and formulate the expression for an nth term. There is also a mention of the expansion of sinx about x=0 and how it relates to the exercise.
  • #1
mundane
56
0

Homework Statement



1. First, calculate the Taylor polynomial of degree 4 for f(x)=sin(3x) about x=0.

2. Then find the 156th term of the infinite Taylor Series for g(x)=sin(3x)

Homework Equations



My Taylor polynomial ended up being -4.5x3+3.

The Attempt at a Solution



I understood part one, but how do I use the nth term for infinite series equation on the polynomial I just developed? Or is it asking something different?
 
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  • #2
From the terms you calculated, look at the pattern of the formulas and see if you can formulate the expression for an nth term.

Then you'd want n=156

If you know the expansion of sinx about x=0 or how to formulate the nth term, it is a similar exercise.
 
  • #3
mundane said:

Homework Statement



1. First, calculate the Taylor polynomial of degree 4 for f(x)=sin(3x) about x=0.

2. Then find the 156th term of the infinite Taylor Series for g(x)=sin(3x)

Homework Equations



My Taylor polynomial ended up being -4.5x3+3.

The Attempt at a Solution



I understood part one, but how do I use the nth term for infinite series equation on the polynomial I just developed? Or is it asking something different?

Your degree 4 Taylor polynomial is also a bit off. Is that just a typo?
 

FAQ: How to find the nth term of this Series.

What is the nth term of a series?

The nth term of a series is the formula or rule that can be used to find the value of any term in the series, including the first term (n=1), second term (n=2), third term (n=3), and so on. It is typically denoted by the letter "a" followed by the term number in subscript (e.g. an).

How do I find the nth term of a series?

To find the nth term of a series, you need to first identify the pattern or rule that the series follows. This could be a numerical pattern (e.g. adding or multiplying by a certain number) or a geometric pattern (e.g. increasing by a common ratio). Once you have identified the pattern, you can use it to create a formula for finding the value of any term in the series.

Can the nth term of a series be a negative number?

Yes, the nth term of a series can be a negative number. This depends on the pattern or rule that the series follows. For example, if the series is a decreasing sequence (e.g. -3, -6, -9, -12...), then the nth term would be a negative number.

What if I can't find a pattern in the series?

If you are having trouble finding a pattern in the series, you may want to try looking at a few more terms to see if a pattern emerges. You can also try graphing the series to see if there is a visual pattern. If you are still unable to find a pattern, it is possible that the series is a random or non-repeating sequence, in which case there may not be a formula for finding the nth term.

Can I use different methods to find the nth term of a series?

Yes, there are multiple methods that can be used to find the nth term of a series. Some common methods include using a table to list out the terms and look for a pattern, using algebraic manipulation to create a formula, or using geometric patterns and ratios. The method you use may depend on the type of series and your personal preference.

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