Solving a Sequence to Find an Equation

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In summary: I should have known that factorials would work and I'm just so stupid. In summary, the problem is extremely easy, but the equation for the nth term is not clicking in my head.
  • #1
Phyzwizz
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I know this problem probably extremely easy, and I can see the pattern of the sequence but I can't seem to figure out how to represent that pattern as an equation.

The sequence is 1-1/2+1/6-1/24+1/120...
Now I obviously see that to get the next term you multiply the previous term by 1/n
but doing this doesn't allow me to obtain "1" the very first term because I don't know the terms before it making all terms after it uncertain through this method.
The closest equation I've gotten is :

an=(1/(n(an-1)))(-1)n+1
using this I can obtain everything but the first term 1. I'm certain there must be another equation that is just not clicking in my head.
 
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  • #2
Phyzwizz said:
I know this problem probably extremely easy, and I can see the pattern of the sequence but I can't seem to figure out how to represent that pattern as an equation.

The sequence is 1-1/2+1/6-1/24+1/120...
That isn't a sequence - it's an infinite series. A sequence is a list of numbers. In this case the sequence is {1, -1/2, 1/6, -1/24, 1/120, ...}

An infinite series is the sum of the terms in a sequence.

What are you trying to do in this problem, find the nth term in the sequence or add up the terms in the series? I would imagine that all you need to do is find the equation of the nth term in the sequence.
Phyzwizz said:
Now I obviously see that to get the next term you multiply the previous term by 1/n
but doing this doesn't allow me to obtain "1" the very first term because I don't know the terms before it making all terms after it uncertain through this method.
The closest equation I've gotten is :

an=(1/(n(an-1)))(-1)n+1
using this I can obtain everything but the first term 1. I'm certain there must be another equation that is just not clicking in my head.

Do you know about the factorial function? n! = 1 * 2 * 3 * ... * (n - 1) * n.
 
  • #3
For this problem I am supposed to put the infinite series in sigma notation.
Yes I am aware of factorials and wow I just solved it. I can't believe I missed that, that's terrible.

an=1/n!(-1)n+1...

Wow I'm really angry at myself.
 

FAQ: Solving a Sequence to Find an Equation

What is a sequence and how do you solve it to find an equation?

A sequence is a list of numbers that follow a specific pattern or rule. To solve a sequence and find an equation, you need to identify the pattern and use it to create a general rule or formula that can generate all the numbers in the sequence.

What are the steps involved in solving a sequence to find an equation?

The steps for solving a sequence to find an equation are:

  • Observe the given numbers and look for a pattern or rule.
  • Write down the general form of the pattern.
  • Use the general form to create an equation that will generate the given numbers.
  • Test the equation by plugging in different numbers from the sequence.
  • If the equation generates all the numbers in the sequence, then it is the correct equation. If not, revise the equation until it fits all the numbers.

What are some common types of patterns that can be found in a sequence?

Some common types of patterns found in a sequence include arithmetic sequences (where there is a constant difference between each term), geometric sequences (where there is a constant ratio between each term), and quadratic sequences (where the difference between terms follows a pattern of a quadratic equation).

What are some tips for solving a sequence to find an equation?

Some tips for solving a sequence to find an equation include:

  • Start by writing out the given numbers in a clear and organized way.
  • Look for trends and patterns in the numbers, such as differences between terms or common factors.
  • Try to think of a general formula or rule that could generate the numbers in the sequence.
  • Check your equation by plugging in different numbers from the sequence to see if it generates the correct result.
  • If you are stuck, try working backwards from the answer to see if you can find a pattern that fits the sequence.

How can solving a sequence to find an equation be useful in real life?

Solving a sequence to find an equation can be useful in various fields such as mathematics, physics, and computer science. It can help in predicting future values, analyzing patterns and trends, and creating models for real-life phenomena. For example, it can be used to predict future stock prices, analyze population growth, or design algorithms for computer programs.

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