Question

a series is absolutely convergent if sum of the series is : finite or zero or infinity

Answer 1

A very important class of finite series, more important than the harmonic ones, are the geometric series. (2.2) ... of terms tends to infinity: an infinite series is defined to be the limit of its sequence of partial sums. Example 2.5. ... For x ∈ R, the (infinite) geometric series ∑n≥0 xn converges if |x| < 1 and diverges if |x| ≥ 1.