(a) Explain why, when proving the convergence of a series it is permissible to ignore finitely many terms of the series.
(b) Use (a) together with a form of the comparison test to show that the series converges.
Let be the th partial sum. The series converges iff the sequence of partial sums converges.
Now suppose that is the partial sum formed by ignoring the first entries and as . Then and by continuity of the operation of adding the constant value . So the original series also converges.