A convergent series is a mathematical series in which the sum of its terms approaches a finite value as the number of terms increases.
The sum of a convergent series can be found by using a specific formula, such as the geometric series formula or the telescoping series formula.
The formula for finding the sum of the series t^(-n^2) is given by S = t^(-1) + t^(-4) + t^(-9) + ... + t^(-n^2), where n = 1 to ∞.
No, the sum of a convergent series cannot be negative. A convergent series must approach a finite value, which means it cannot have a negative sum.
The sum of the series t^(-n^2) for n=1 to ∞ can be used in various mathematical and scientific applications, such as calculating probabilities in statistical models or determining the stability of a system in physics.