Efficient Steps for Closed Form Summation: A Detailed Guide | 1.7^k and 2k"

In summary, the conversation is about finding the correct formula for a given problem. The person initially presents their steps and expresses uncertainty about their solution. They mention using two different forms for different parts of the problem and provide the final answer they got. They ask for confirmation and someone suggests verifying their answer with other values. In the end, the person realizes their answer is correct and thanks the other person.
  • #1
mohabitar
140
0
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So here are my steps, which for some reason I feel are very wrong:

Well in closed form would be [n(n+1)]/2 so 2k would be 2*[n(n+1)]/2
For 1.7^k, I used a different form, which I don't have the formula for in front of me, but the final result for that part is [1.7^(n+1) - 1] /[1.7 - 1]

So the final answer I got was [2*[n(n+1)]/2] + [1.7^(n+1) - 1] /[1.7 - 1]

This feels incorrect to me for some reason. Can anyone confirm this or maybe this is correct?
 
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  • #2
You can check it yourself. Try a few sums for different values of n and see if the formula you derived gives the same answer. If it does, you can be reasonably sure you have the correct result.
 
  • #3
Well duh I don't know why I didnt think of that. Turns out my answer is correct. Thanks!
 

FAQ: Efficient Steps for Closed Form Summation: A Detailed Guide | 1.7^k and 2k"

What is closed form summation?

Closed form summation is a method used to find the sum of a series of numbers by using a formula, rather than adding each individual number. This can be more efficient and accurate for larger series.

How do I calculate closed form summation?

To calculate closed form summation, you need to first identify the formula for the series, which typically involves finding a pattern in the numbers. Once you have the formula, you can plug in the starting and ending values of the series to find the sum.

What is the significance of 1.7^k and 2k in closed form summation?

1.7^k and 2k are commonly used as examples in closed form summation because they demonstrate different types of series. 1.7^k represents a geometric series, where each term is multiplied by a common ratio, while 2k represents an arithmetic series, where each term is added by a constant value.

Can closed form summation be used for all types of series?

No, closed form summation works best for series that follow a specific pattern or formula. It may not be applicable for series with random or irregular numbers.

How is closed form summation different from other summation methods?

Closed form summation is different from other summation methods, such as using a calculator or adding each individual number, because it provides a more efficient and accurate way to find the sum of a series by using a formula.

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