# Evaluating a Finite Sum to a Closed Form Expression

• aaaa202
In summary, there is a trick to evaluate this sum to a closed form expression by treating it as an integral and breaking it into a difference of two integrals. The first integral corresponds to a geometric series and the second becomes a constant times an integral of e raised to the power of a quadratic function.
aaaa202
I have a finite sum of the form:

n=1Nexp(an+b√(n))

Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.

aaaa202 said:
I have a finite sum of the form:

n=1Nexp(an+b√(n))

Is there any trick to evalute this sum to a closed form expression? e.g. like when a finite geometric series is evaluated in closed form.
Not here.
You can often get a clue by treating a sum as an integral. In this case you can break it into a difference of two integrals. The first corresponds to ∑n=1Nexp(an), which is simply the sum of a geometric series, but the second becomes constant*∫eax2.dx.

## 1. What is a finite sum?

A finite sum is a mathematical expression that involves adding a finite number of terms together. For example, 1+2+3+4 is a finite sum with 4 terms.

## 2. 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 and functions, such as addition, subtraction, multiplication, division, exponentiation, and logarithms. It does not involve infinite operations or functions.

## 3. Why is it important to evaluate a finite sum to a closed form expression?

Evaluating a finite sum to a closed form expression allows for a more concise and efficient representation of the sum. It also allows for easier manipulation and analysis of the sum's properties.

## 4. How do you evaluate a finite sum to a closed form expression?

The process of evaluating a finite sum to a closed form expression involves identifying any patterns or relationships between the terms, using known formulas and identities, and simplifying the expression until it can be written in a closed form.

## 5. Are there any limitations to evaluating a finite sum to a closed form expression?

Yes, there are some finite sums that cannot be evaluated to a closed form expression. This is because they involve complex or irregular patterns that cannot be simplified using known formulas and identities. In these cases, the finite sum can still be represented in a concise and efficient manner using sigma notation.

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