Final answer:
The question to find the interval of convergence for the series Σ(5)² is incomplete without further detail on the nature of the series. To find the interval of convergence, more information, such as the dependence of terms on a variable, is required. Convergence tests such as the ratio test or the root test are typically employed to find this interval for power series.
Step-by-step explanation:
The student has asked to find the interval of convergence for the series Σ(5)². However, without additional context or information about the format of the series, it's not possible to provide a direct answer. Normally, the convergence of a series depends on the specific form it takes, such as a power series, geometric series, or another type. For example, if the series is constant, like Σ(5)², and the common term does not depend on the variable of summation, the series diverges unless the common term is zero, because the sum will approach infinity.
If this was meant to be a power series of the form Σ((5x)^n) for some variable x, then we would use tests like the ratio test or the root test to determine convergence. For instance, a power series Σ(an*x^n) converges absolutely if the limit of |a(n+1)x^(n+1)/(an*x^n)| as n approaches infinity is less than 1 for a given x, and similarly for the root test using the limit of the nth root of |an*x^n|.