DLMF:3.9.E5 (Q1390)

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DLMF:3.9.E5
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    Statements

    Defining formula
    ln ⁡ 2 = 1 - 1 2 + 1 3 - 1 4 + ⋯ = 1 1 ⋅ 2 1 + 1 2 ⋅ 2 2 + 1 3 ⋅ 2 3 + ⋯ , 2 1 1 2 1 3 1 4 ⋯ 1 ⋅ 1 superscript 2 1 1 ⋅ 2 superscript 2 2 1 ⋅ 3 superscript 2 3 ⋯ {\displaystyle{\displaystyle\ln 2=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots% =\frac{1}{1\cdot 2^{1}}+\frac{1}{2\cdot 2^{2}}+\frac{1}{3\cdot 2^{3}}+\cdots,}}
    0 references
    DLMF id
    DLMF:3.9.E5
    0 references
    Symbols used
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
     
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