Propositions from Infinite series
All propositions from Infinite series.
Finite changes do not affect convergence
Adding, removing or changing finitely many terms does not affect whether a series converges. If two series converge, their termwise sum and scalar multiples also converge.
Changing finitely many terms changes the partial sums by a fixed amount after the changed terms have been passed. A fixed amount can change the sum, but not whether the partial-sum sequence has a finite limit.
- [1]:Infinite series