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Summation question......Plz help

\( \sum_{i=1}^\infty (-1)^i \) * \( \frac {1}{i} \)

I encountered this problem while doing a physics sum of magnetic fields..Please reply soon and Yeah..Thanks for your answers..

Note by Rushi Rokad
3 years, 10 months ago

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\( \displaystyle \sum_{i=1}^{\infty} \dfrac{(-1)^i}{i} = -\log{2}\) Gopinath No · 3 years, 10 months ago

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@Gopinath No can you please explain ? Rushi Rokad · 3 years, 10 months ago

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@Rushi Rokad \( \displaystyle \ln(1+x)=x-\frac{x^2}{2}+\frac{x^3}{3}-\frac{x^4}{4}+..... \)

Looks familiar? Pranav Arora · 3 years, 10 months ago

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@Pranav Arora Thanks. Rushi Rokad · 3 years, 10 months ago

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by taylor series we have -log(1+y)= - y + (y^2)/2 + (y^3)/3........ which generates the above pattern by putting y=1 hence the answer for this is -log2 which would be around -0.30103 .. :) Ramesh Goenka · 3 years, 10 months ago

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@Ramesh Goenka Thanks. Rushi Rokad · 3 years, 10 months ago

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