Finding the General Term for a Sequence with a Given Sum?

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So, in summary, the general term of the sequence is -2/n(n-1)(n+1), derived from T(n)=S(n)-S(n-1), and T(1) can be calculated directly from the general expression for S(n) when n=1. There is no such thing as S(0) because a sum cannot have 0 terms.
  • #1
LAdidadida
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Homework Statement



Find the general term of a sequence whose sum of the first n terms is S(n)=1/n(n+1)

Homework Equations



N/A

The Attempt at a Solution



I am able to work out T(n) as through T(n)=S(n)-S(n-1)
which works out to be -2/n(n-1)(n+1) however this doesn't work for when n=1

Any help would be greatly appreciated :smile:
 
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  • #2
LAdidadida said:

Homework Statement



Find the general term of a sequence whose sum of the first n terms is S(n)=1/n(n+1)

Homework Equations



N/A

The Attempt at a Solution



I am able to work out T(n) as through T(n)=S(n)-S(n-1)
which works out to be -2/n(n-1)(n+1) however this doesn't work for when n=1

Any help would be greatly appreciated :smile:

expression you derived is from T(n)=S(n)-S(n-1) => T(1)=S(1)-S(0)
T(1)=S(1) , S(0) doesn't make sense.

T(1) can be directly calculated from general expression for S(n) for n=1
 
  • #3
In other words, since a sum cannot have 0 terms, there is no such thing as S(0)! The first partial sum is S(1)= T(1).
 

Related to Finding the General Term for a Sequence with a Given Sum?

What is a sequence question?

A sequence question is a type of question that requires the respondent to provide a specific order or arrangement of items or events. It can be used to assess a person's ability to organize information or to understand cause and effect relationships.

What types of sequences are commonly used in sequence questions?

Some common types of sequences used in sequence questions include numerical sequences, alphabetical sequences, and chronological sequences. Other types may involve patterns or relationships between objects or events.

How can I improve my ability to answer sequence questions?

One way to improve your ability to answer sequence questions is to practice regularly with different types of sequences. This can help you become more familiar with the patterns and relationships that may be present. You can also try breaking down the sequence into smaller parts and identifying any rules or patterns that may help you determine the correct answer.

Are there any strategies for answering sequence questions?

Yes, there are several strategies that can be helpful for answering sequence questions. Some common strategies include looking for patterns or relationships, using process of elimination, and checking for any rules or logic that may apply to the sequence. It can also be helpful to read the question carefully and pay attention to any clues or keywords that may indicate the correct answer.

What are some common mistakes to avoid when answering sequence questions?

One common mistake to avoid when answering sequence questions is jumping to conclusions without fully understanding the sequence or the question. It is important to carefully read and analyze the given information before selecting an answer. It can also be helpful to double check your answer and make sure it follows the established rules or patterns of the sequence.

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