SUMMARY
The limit of the recursive succession defined by a1 = sqrt(b) and an+1 = sqrt(b + an) converges to a solution of the polynomial equation x^2 - x - b = 0, where b > 0. Assuming the sequence has a limit, both lim a_(n+1) and lim a_n equal x. The solutions to this polynomial provide the limits of the succession.
PREREQUISITES
- Understanding of recursive sequences
- Knowledge of limits in calculus
- Familiarity with solving quadratic equations
- Basic algebraic manipulation skills
NEXT STEPS
- Study the properties of recursive sequences in calculus
- Learn about convergence criteria for sequences
- Explore the quadratic formula and its applications
- Investigate fixed-point iteration methods
USEFUL FOR
Students studying calculus, mathematicians interested in recursive functions, and educators teaching limit concepts in sequences.