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right the denominators keep getting
bigger and bigger but the numerators
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bigger and bigger but the numerators
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bigger and bigger but the numerators
stay the same they're always always X so
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stay the same they're always always X so
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stay the same they're always always X so
when I take the product if I go far
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when I take the product if I go far
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when I take the product if I go far
enough out I'm going to be multiplying
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enough out I'm going to be multiplying
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enough out I'm going to be multiplying
by very very small numbers more and more
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by very very small numbers more and more
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by very very small numbers more and more
of them and so no matter what X is these
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of them and so no matter what X is these
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of them and so no matter what X is these
numbers will converge to 0 they'll get
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numbers will converge to 0 they'll get
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numbers will converge to 0 they'll get
smaller and smaller as X gets to be
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smaller and smaller as X gets to be
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smaller and smaller as X gets to be
bigger
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bigger
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bigger
that's the sign that X is inside of the
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that's the sign that X is inside of the
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that's the sign that X is inside of the
radius of convergence this is the sign
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radius of convergence this is the sign
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radius of convergence this is the sign
for you that that this series converges
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for you that that this series converges
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for you that that this series converges
for that value of X and because I could
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