Answer
See below.
Work Step by Step
See text: "Adding or Deleting Terms" in section 2, following Th.8.
The convergence or divergence of a series is determined by the "tail-end" of the sequence of partial sums, not the first few.
Adding or deleting a finite number of terms does not change whether the series is convergent or not.
A divergent series will remain divergent.
A convergent series will remain convergent, but since we have extra terms or have thrown out some terms of the sum, the actual sum will change.
