Closed Form Evaluation of Sigma Notation with Exponential and Polynomial Terms

In summary, Sigma-evaluate in closed form is a mathematical concept used to find the exact value of a summation expression, commonly used in scientific calculations. It is important for accurate and simplified results, and can be calculated using a specific formula. Some common applications include finding the area under a curve and solving equations. However, there may be limitations in finding an exact solution for certain expressions, requiring the use of numerical approximations or other methods.
  • #1
m0286
63
0
Hello
I have another question:
It says: Evaluate in closed form
n(sigma)i=1 (2^i - i^2)

(The n is above the sigma and the i=1 is below)
what i did so far is:
(sigma)2*2^i-1 (sigma)i^2
=(2(2^n -1)/2-1) - (n(n+1)(2n+1)/6)

now do I need to do something else to shorten this down... if so can someone help me with it...
THANKS!
 
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  • #2
That's already pretty much simplified. If you had to do anything to that, you might take the 2 inside the numerator of the first fraction.
 

FAQ: Closed Form Evaluation of Sigma Notation with Exponential and Polynomial Terms

What is Sigma-evaluate in closed form?

Sigma-evaluate in closed form is a mathematical concept that involves finding the exact value of a summation expression, rather than using a numerical approximation. It is often used in scientific calculations to obtain precise results.

Why is Sigma-evaluate in closed form important?

Sigma-evaluate in closed form is important because it allows for accurate and exact calculations in scientific research. It also helps in simplifying complex mathematical expressions, making them easier to understand and work with.

How do you calculate Sigma-evaluate in closed form?

To calculate Sigma-evaluate in closed form, you need to use the specific formula for the summation expression. This formula can vary depending on the variables and limits of the summation. Once you have the formula, you can plug in the values and solve for the exact result.

What are some common applications of Sigma-evaluate in closed form?

Sigma-evaluate in closed form is commonly used in various scientific fields, such as physics, engineering, and statistics. It can be applied to calculate the area under a curve, determine the probability of an event, and solve equations involving finite sums.

Are there any limitations of Sigma-evaluate in closed form?

One limitation of Sigma-evaluate in closed form is that it may not always be possible to find an exact solution for a given summation expression. In such cases, numerical approximations or other mathematical methods may be used to obtain an approximate solution.

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