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Zeno's Paradox suggests you can never reach your destination because you must first cover half the distance, then half of the remaining distance, and so on. This raises the question of whether you can add infinitely many numbers. In mathematics, a series is the sum of a sequence. A series converges if the sequence of its partial sums converges to a finite limit. For example, a geometric series demonstrates convergence. We will explore the conditions under which series diverge and converge, ultimately resolving Zeno's paradox.
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Zeno’s Paradox You can’t actually get anywhere because you always have to cover half the remaining distance! You have to do half, then half that.. etc. Can you add infinitely many numbers ??
Informal Definition A series is sequence added up.
Formal Definition A series converges if the sequence of partial sums converges.
Definition is a geometric series.
Theorem Diverges if Convergesto if
Proof: If and only if
Telescoping Series Use Partial Fractions
