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.