Computing Upper & Lower Limit of {Sn} from Expression

In summary, the user is asking for a way to compute the Upper and Lower limit of {Sn} directly from its expression instead of by deduction of the terms. They are given a hint to deal with the even and odd terms separately and are advised to write out equations with only even and odd terms in order to simplify the process. The user is grateful for the help and is encouraged to come back for more assistance if needed. The conversation ends with a comment about successfully using a feature called "size."
  • #1
Ka Yan
27
0
How can I compute the Upper and Lower limit of {Sn}, which defineded as: S1 = 0, S2m = S2m-1 /2, S2m+1 = 1/2 + S2m , directly from its expression, rather than by deduction of the terms?

(i.e., from the definition of Sn, instead of from 0, 0, 1/2, 1/4, 3/4, ...)

thks!
 
Last edited:
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  • #2
Hi, Ka Yan! :smile:

Hint: deal with the even and odd terms separately.

That is, get an equation with only even terms in it, and another with only odd terms in it.

Instead of one series with two rules, that should give you two series each with only one rule, which is much easier! :smile:
 
  • #3
I got you!
That you mean, write S2m+1 = 1/2 + S2m-1 /2, and S2m+2 = (1/2 + S2m) /2 instead, isn't it?

Thank you!
 
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  • #4
You're very welcome! :smile:

I assume you can finish it now, but if you can't after a few hours, come back for another hint! :smile:

[size=-2]ooh, you've worked out how to use "size"! :smile:[/size]​
 

Related to Computing Upper & Lower Limit of {Sn} from Expression

1. What is the purpose of computing the upper and lower limit of {Sn} from an expression?

The purpose of computing the upper and lower limit of {Sn} from an expression is to determine the maximum and minimum possible values of {Sn} based on the given expression. This can help in analyzing the behavior and range of {Sn} and can also provide valuable information for further calculations and comparisons.

2. How do you compute the upper and lower limit of {Sn} from an expression?

To compute the upper and lower limit of {Sn} from an expression, you can use the formula: Upper Limit = n(a + b), Lower Limit = n(a - b) where n represents the number of terms in the expression, and a and b represent the first and last terms of the expression, respectively.

3. Can the upper and lower limit of {Sn} be the same?

Yes, the upper and lower limit of {Sn} can be the same. This would happen when all the terms in the expression have the same value. In this case, the expression would have a constant value, and the upper and lower limit would be equal to that value multiplied by n.

4. Are there any restrictions on the values of {Sn} when computing the upper and lower limit?

There are no restrictions on the values of {Sn} when computing the upper and lower limit. However, it is important to note that the expression must have a finite number of terms in order for the limits to be well-defined.

5. How can computing the upper and lower limit of {Sn} from an expression be useful in real-world applications?

Computing the upper and lower limit of {Sn} from an expression can be useful in various real-world applications, such as in statistics, finance, and engineering. It can help in analyzing data and making predictions, evaluating investment risks, and designing structures with specific performance limits, among others.

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