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matrix_204
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how do i show that 1/(n+1)<=ln(1+1/n)<=1/n? i need sum help, i have the definitions for log n e except i need to kno how to apply them, at first it seemed simple to just do it but i m havin sum trouble..
matrix_204 said:how do i show that 1/(n+1)<=ln(1+1/n)<=1/n? i need sum help, i have the definitions for log n e except i need to kno how to apply them, at first it seemed simple to just do it but i m havin sum trouble..
You've already solved this problem! Let x=(1 + 1/n) and go here:matrix_204 said:how do i show that 1/(n+1)<=ln(1+1/n)<=1/n? i need sum help, i have the definitions for log n e except i need to kno how to apply them, at first it seemed simple to just do it but i m havin sum trouble..
The purpose of proving this inequality is to establish a relationship between two mathematical expressions, and to demonstrate that one expression is always greater than or equal to the other for a given range of values.
This inequality is important because it is a fundamental mathematical concept that has many real-world applications. It is used in fields such as economics, physics, and computer science to model and analyze various phenomena.
This inequality can be proven using various mathematical techniques such as induction, calculus, or algebraic manipulation. The specific method used may depend on the context and purpose of the proof.
The implications of this inequality are that the expression 1/(n+1) can be used as an upper bound for the natural logarithm of 1+1/n, and vice versa. This can be useful in solving mathematical problems and making approximations.
Yes, this inequality can be generalized to other expressions by substituting different functions or variables into the original inequality. However, the validity of the inequality may depend on the specific values of the functions or variables used.