Final answer:
To evaluate the indefinite integral as a power series, the given function can be expressed as a power series using the geometric series formula. The series converges for |t^10| < 1, so the radius of convergence is 1.
Step-by-step explanation:
In order to evaluate the indefinite integral as a power series, we need to express the function as a power series first. We can do this by using the geometric series formula, which states that 1/(1-x) = 1 + x + x^2 + x^3 + ... for |x| < 1.
In our case, we have ∫ (t/(1-t^10)) dt. We can rewrite the denominator as 1 - t^10, which is in the form of a geometric series with x = t^10. So, we can express the function as a power series: ∫ (t/(1-t^10)) dt = ∫ (t∑(n=0 to ∞) (t^10)^n) dt = ∫ (t∑(n=0 to ∞) t^(10n)) dt.
To find the radius of convergence R, we can use the ratio test. The ratio test states that if lim (n→∞) |a_(n+1)/a_n| < 1, the series converges. In our case, a_n = t^(10n), so a_(n+1) = t^(10(n+1)).
Using the ratio test, we have lim (n→∞) |t^(10(n+1))/t^(10n)| = lim (n→∞) |t^10| = |t^10| < 1. This means that the series converges for |t^10| < 1. Therefore, the radius of convergence is R = 1.