Learn the Summation Formula for a>1: A Quick Guide | N=0 to N"

In summary, a summation formula is a mathematical expression denoted by the Greek letter sigma (Σ) that represents the sum of a series of numbers. To use it, you need to determine the starting and ending values of the series, plug them into the formula, and evaluate the expression. There are various types of summation formulas, including arithmetic, geometric, telescoping, infinite, and power series. They can be applied to solve real-world problems in fields such as finance, engineering, and physics. To ensure correct application, you can double-check with a calculator or use mathematical induction to prove the validity of the formula.
  • #1
amaresh92
163
0
whats the summation of a^n for a>1 over summation n=0 to N
thanks.
 
Physics news on Phys.org
  • #2
amaresh92 said:
whats the summation of a^n for a>1 over summation n=0 to N
thanks.

Hint: for [itex]\,r\neq 1\,[/itex] a constant, we have

$$\sum_{n=0}^mr^n=\frac{r^{m+1}-1}{r-1}$$

DonAntonio
 
  • #3
This is the sort of thing most people just look that up - do you need to work out the formula or what?
 

1. What is a summation formula?

A summation formula is a mathematical expression that represents the sum of a series of numbers. It is often denoted by the Greek letter sigma (Σ) and includes a variable, a starting value, an ending value, and an expression to be evaluated.

2. How do I use a summation formula?

To use a summation formula, you need to determine the starting and ending values of the series and plug them into the formula. Then, substitute the variable in the formula with the values from the series and evaluate the expression. Finally, add up all the results to get the sum of the series.

3. What are the common types of summation formulas?

Some common types of summation formulas include arithmetic series, geometric series, and telescoping series. Other types include infinite series and power series, which are used in calculus and other advanced mathematical concepts.

4. Can summation formulas be used to solve real-world problems?

Yes, summation formulas can be used to solve real-world problems in various fields such as finance, engineering, and physics. For example, they can be used to calculate the total cost of an investment or the amount of energy generated by a power plant.

5. How do I know if I have applied a summation formula correctly?

To verify if a summation formula has been applied correctly, you can double-check your calculations by using a calculator or a spreadsheet program. Additionally, you can also use mathematical induction to prove the validity of the formula for all values of the variable.

Similar threads

  • Precalculus Mathematics Homework Help
Replies
17
Views
1K
  • Precalculus Mathematics Homework Help
Replies
7
Views
808
  • Precalculus Mathematics Homework Help
Replies
5
Views
1K
  • General Math
Replies
6
Views
828
  • Precalculus Mathematics Homework Help
Replies
6
Views
1K
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
  • General Math
Replies
5
Views
941
  • Precalculus Mathematics Homework Help
Replies
6
Views
693
  • Precalculus Mathematics Homework Help
Replies
14
Views
556
  • Precalculus Mathematics Homework Help
Replies
2
Views
1K
Back
Top