Sure, but how useful it is, I don't know.GreenPrint said:Sense e^x=Ʃ[k=0,∞] x^k/k!
then
ln(e^x) = ln(Ʃ[k=0,∞] x^k/k!)
x = ln(Ʃ[k=0,∞] x^k/k!)
is this true?
Mark44 said:Sure, but how useful it is, I don't know.
I sense that you don't understand the difference between sense and since.
An infinite series in calculus 2 is a sum of an infinite number of terms. It is represented by the notation Σ (sigma) and is used to approximate the value of a function or to find the sum of a sequence.
The convergence of an infinite series can be determined by using various convergence tests such as the comparison test, ratio test, root test, and integral test. These tests involve comparing the given series to known convergent or divergent series and using their properties to determine the convergence of the given series.
A convergent infinite series is one that has a finite sum or limit, meaning the terms in the series eventually get smaller and smaller and approach a specific value. On the other hand, a divergent infinite series is one that does not have a finite sum or limit, meaning the terms in the series do not approach a specific value and the series either grows infinitely or oscillates.
The sum of an infinite series is calculated by taking the limit of the partial sums of the series as the number of terms approaches infinity. This process is known as finding the limit of the sequence of partial sums, and the resulting value is the sum of the infinite series.
Calculus 2, specifically infinite series, is used in various real-world applications such as physics, engineering, and economics. It is used to model and analyze continuous systems, such as motion, population growth, and economic trends, where the variables are constantly changing. It also plays a crucial role in signal processing, control theory, and optimization problems.