Mattofix said:thanks - yeah, sorry i havnt shown any working- i know it converegs to 1 though.
Exponential convergence is a mathematical concept that describes the behavior of a sequence or function as it approaches a limit. It occurs when the terms of the sequence or function decrease or increase at a constant rate, resulting in a rapid approach to the limit.
Exponential convergence is a type of geometric convergence, which is characterized by a constant ratio between successive terms. It is different from arithmetic convergence, where the difference between successive terms is constant, and logarithmic convergence, where the terms decrease or increase at a decreasing rate.
Exponential convergence is commonly used in fields such as physics, engineering, and finance to model natural phenomena and make predictions. For example, it can be used to model population growth, radioactive decay, and compound interest.
The main advantage of exponential convergence is its speed. As the terms of the sequence or function approach the limit at a constant rate, the convergence is rapid and efficient. This makes it a useful tool for solving problems and making predictions.
While exponential convergence is a powerful tool, it does have some limitations. It can only be applied to sequences or functions that have a constant ratio between successive terms. Additionally, it may not accurately model certain real-world phenomena that do not exhibit a constant rate of change.