Prove that if a series is convergent, then its partial sums, s_n, are bounded.
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A more direct way would warrant this. Let . So then for to converge to a finite value, let's say , we must have that . But now assuming that we are talking about we have that the defintion of a sequence converging to is for every there exists a such that . Now since are real there exists a number let say such that . So it follows that . Thus it is bounded.