)darkmagic said:
) write it as Im(∑ einπt) Summation with infinity is a mathematical concept that involves adding an infinite number of terms together. It is also known as an infinite series or an infinite sum.
The calculation of summation with infinity involves finding the limit of a sequence of partial sums, where each partial sum is the sum of a finite number of terms in the series. This limit is the value of the infinite series.
Some common examples of summation with infinity include geometric series, harmonic series, and power series. These types of series have specific formulas for calculating their infinite sums.
Summation with infinity is important in mathematics because it allows us to represent and manipulate infinite quantities. It is also used in various fields, such as calculus, physics, and statistics, to solve problems and make predictions.
No, it is not possible to have a finite sum with an infinite number of terms. This is because as the number of terms increases, the sum also increases without bound, reaching infinity. However, certain infinite series may converge to a finite value, but this is not the same as having a finite sum.