- #1
dannysaf
- 10
- 0
Consider the sequence xn in which xn = 1/2(xn−1 + (3/xn-1) and x1 = a
(a not equals 0). Find lim n →∞ xn
(a not equals 0). Find lim n →∞ xn
Find Limit of Xn as n Approaches Infinity
- Thread starter dannysaf
- Start date
-
- Tags
- Limit
Click For Summary
SUMMARY
The discussion focuses on finding the limit of the sequence defined by the recurrence relation xn = 1/2(xn-1 + (3/xn-1)) with the initial condition x1 = a, where a is a non-zero constant. Participants analyze the behavior of the sequence as n approaches infinity, ultimately concluding that the limit exists and can be determined by solving the equation x = 1/2(x + (3/x)). The limit is found to be √3, which is derived from the fixed point of the recurrence relation.
PREREQUISITES- Understanding of sequences and limits in calculus
- Familiarity with recurrence relations
- Basic algebra for solving equations
- Knowledge of fixed points in mathematical analysis
- Study the concept of fixed points in iterative sequences
- Learn about convergence criteria for sequences
- Explore advanced topics in recurrence relations
- Investigate the application of limits in real analysis
Students of calculus, mathematicians interested in sequences, and educators teaching limit concepts will benefit from this discussion.
Similar threads
- · Replies 10 ·
- · Replies 15 ·
- · Replies 17 ·
- · Replies 6 ·
- · Replies 3 ·