Today's counter-intuitive fact is brought to you by the Natural Logarithm.pic.twitter.com/lphAcxseQ4
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Another way to see it is to write ln(2ⁿ) = n*ln(2) and realize that ln(1-x) = -Σxⁿ/n and let x=1/2.
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heyoo that's a good one! This was just the first thing I came up with
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Because two infinite series converge to the same number can we equate them? What are we exactly equating? The convergence or the infinite series?
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The Infinite series, but of course they must also both then converge
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I think this proof is not full. We shall prove Σ 1/(2^n*ln2^n) is uniformly convergent.
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Twitter proofs leave the proof of uniform convergence as an exercise to the reader.
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The write-thing-as-an-exponential-integral trick is a CLASSIC QFT BOI thing.
Thanks. Twitter will use this to make your timeline better. UndoUndo
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