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

  • Thread starter Thread starter amaresh92
  • Start date Start date
  • Tags Tags
    Formula Summation
Click For Summary
SUMMARY

The summation formula for a geometric series where \( a > 1 \) and \( n \) ranges from 0 to \( N \) is given by the equation \( \sum_{n=0}^N a^n = \frac{a^{N+1} - 1}{a - 1} \). This formula applies specifically when the common ratio \( a \) is not equal to 1. The discussion emphasizes the importance of understanding this formula for efficient calculations in mathematical contexts.

PREREQUISITES
  • Understanding of geometric series
  • Familiarity with summation notation
  • Basic algebra skills
  • Knowledge of limits and convergence
NEXT STEPS
  • Study the derivation of the geometric series summation formula
  • Explore applications of geometric series in finance and computer science
  • Learn about convergence criteria for infinite series
  • Investigate related summation formulas for different series types
USEFUL FOR

Mathematicians, educators, students in calculus or algebra courses, and anyone involved in quantitative analysis or financial modeling.

amaresh92
Messages
163
Reaction score
0
whats the summation of a^n for a>1 over summation n=0 to N
thanks.
 
Physics news on Phys.org
amaresh92 said:
whats the summation of a^n for a>1 over summation n=0 to N
thanks.

Hint: for \,r\neq 1\, a constant, we have

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

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

Similar threads

Use Euler's summation formula to prove the following....
  • · Replies 17 ·
Replies
17
Views
2K
Prove that ## g(x)=f(x)\log {x}-\int_{2}^{x}t^{-1}f(t)dt ##.
  • · Replies 7 ·
Replies
7
Views
2K
Efficient Methods for Solving Summation Equations: Σ(1/k) - (1/(k+1))
  • · Replies 5 ·
Replies
5
Views
2K
Solve Summation Change of Index: Find $\sum_{k=0}^{n} k^2$
  • · Replies 2 ·
Replies
2
Views
2K
Proof by induction (summation)
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad How Can Nested Summation Functions Be Simplified or Reversed?
  • · Replies 6 ·
Replies
6
Views
2K
Root test proof using Law of Algebra
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Why is Griffiths Treating the Summation Like This?
  • · Replies 4 ·
Replies
4
Views
863
Graduate Summation simpilification process
  • · Replies 5 ·
Replies
5
Views
1K
Product of Two Summations for Matrices and Vectors
  • · Replies 11 ·
Replies
11
Views
7K