SUMMARY
The limit of (1-1/n)^n as n approaches infinity is e^-1, which equals approximately 0.367879. This conclusion is derived from the general limit property lim n goes to infinity (1+x/n)^n = e^x, where x is -1 in this case. Understanding this limit requires familiarity with the definition of the mathematical constant e and its properties in calculus.
PREREQUISITES
- Understanding of limits in calculus
- Familiarity with the exponential function e
- Knowledge of the binomial theorem
- Basic algebraic manipulation skills
NEXT STEPS
- Study the derivation of the limit lim n goes to infinity (1+x/n)^n = e^x
- Explore the properties and applications of the constant e in calculus
- Learn about the binomial theorem and its relevance to limits
- Practice solving limits involving exponential functions
USEFUL FOR
Students studying calculus, mathematics educators, and anyone interested in understanding limits and exponential functions.