apiwowar said:i was thinking that but could that work since that's not a power series?
apiwowar said:wait nevermind, i was confusing myself.
so what I am talking about would be the closed form for the taylor series e^2 then, right?
A sum of infinite series is the sum of all terms in a sequence that continues infinitely. This means that there is no specific end point or final term in the sequence.
The sum of an infinite series can be found using various methods such as the geometric series formula, telescoping series, or convergence tests. Each method may be more suitable for different types of series.
Yes, the sum of an infinite series can be finite. This occurs when the terms in the series decrease in value as the series progresses, eventually approaching zero. In this case, the sum can be calculated by taking the limit of the series.
Understanding infinite series is crucial in various fields such as mathematics, physics, and engineering. It allows for the analysis and prediction of continuous processes and phenomena, and is used in many real-world applications.
Yes, there are many real-life examples of infinite series. Some common examples include calculating compound interest, estimating the value of pi, and predicting population growth. Infinite series can also be used in physics to model natural processes such as radioactive decay.