Can you check to see if i expressed the sums in closed form correctly?

In summary, a closed form expression is a mathematical expression that can be written using a finite number of standard mathematical operations and is important to check for accuracy because it can provide a more efficient way to represent a mathematical concept and errors can lead to incorrect solutions. To check if a sum is expressed in closed form correctly, one should verify that it only uses allowed operations and does not contain infinite or recursive elements, and can also try plugging in different values to compare results. Some common mistakes when expressing sums in closed form include using incorrect operations, forgetting variables or constants, and including infinite or recursive elements. It is possible for a sum to have multiple closed form expressions, but it is important to choose the most appropriate one for the given situation.
  • #1
mr_coffee
1,629
1
Hello everyone, I was wondering if someone can double check my work for #'s 25 and 31.

The directions say:
Express each of the sums in closed form (without using a summation symbol and without using an ellipis...).http://img224.imageshack.us/img224/3514/lastscanle2.jpg
Thanks!
 
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  • #2
You used the index from the sum instead of the limit. So 25 should be 5m not 5i

Also, 31 is (1 + 1/2)n, which means not only should you have gotten 3/2n, but it should have been (3/2)n
 
  • #3
thanks a lot for catching those errors!
 

FAQ: Can you check to see if i expressed the sums in closed form correctly?

What is a closed form expression?

A closed form expression is a mathematical expression that can be written using a finite number of standard mathematical operations such as addition, subtraction, multiplication, division, and exponentiation, as well as constants and variables.

Why is it important to check if a sum is expressed in closed form correctly?

It is important to check because closed form expressions can often be simplified and provide a more efficient way to represent a mathematical concept. Additionally, incorrect expressions can lead to errors in calculations and solutions.

How can I check if my sum is expressed in closed form correctly?

You can check by verifying that the expression only uses the allowed mathematical operations and does not contain any infinite or recursive elements. You can also try plugging in different values for the variables and comparing the results to ensure they match the original sum.

Are there any common mistakes to look out for when expressing sums in closed form?

Some common mistakes include using incorrect mathematical operations, forgetting to include variables or constants, and using infinite or recursive elements.

Can a sum be expressed in multiple closed form expressions?

Yes, a sum can often be expressed in multiple closed form expressions. It is important to choose the most simplified and efficient expression for the specific situation or problem at hand.

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