Expii

# Series Convergence: Ignoring a Finite Number of Terms - Expii

Adding, changing, or removing finitely many summands of an infinite series doesn't affect the convergence/divergence of the series. For example, $$0.5^{-2016} + 2017^{2017} + 0.5^3 + 0.5^4 + 0.5^5 + \dots$$ still converges, because it only differs from the convergent infinite geometric series $$1 + 0.5 + 0.5^2 + 0.5^3 + 0.5^4 + 0.5^5 + \dots$$ in finitely many terms.