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so I'm I've discovered that the natural |
log of 1 plus X is X minus x squared |
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log of 1 plus X is X minus x squared |
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log of 1 plus X is X minus x squared |
over 2 plus X cubed over 3 minus X to |
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over 2 plus X cubed over 3 minus X to |
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over 2 plus X cubed over 3 minus X to |
the fourth over 4 and so on and so on |
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the fourth over 4 and so on and so on |
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the fourth over 4 and so on and so on |
there's the power series expansion for |
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there's the power series expansion for |
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there's the power series expansion for |
the natural log of 1 plus X and |
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the natural log of 1 plus X and |
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the natural log of 1 plus X and |
because I began with a power series |
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because I began with a power series |
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because I began with a power series |
whose radius of convergence was just 1 I |
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whose radius of convergence was just 1 I |
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whose radius of convergence was just 1 I |
began with this power series the radius |
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began with this power series the radius |
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began with this power series the radius |
of convergence of this is also going to |
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of convergence of this is also going to |
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of convergence of this is also going to |
be 1 |
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also because this this function is I |
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also because this this function is I |
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also because this this function is I |
just pointed out this function goes bad |
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just pointed out this function goes bad |
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just pointed out this function goes bad |
when X becomes less than minus 1 so some |
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