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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
4 years, 1 month ago

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\( \displaystyle \sum_{i=1}^{\infty} \dfrac{(-1)^i}{i} = -\log{2}\)

Gopinath No - 4 years, 1 month ago

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can you please explain ?

Rushi Rokad - 4 years, 1 month ago

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

Looks familiar?

Pranav Arora - 4 years, 1 month ago

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@Pranav Arora Thanks.

Rushi Rokad - 4 years, 1 month 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 - 4 years, 1 month ago

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Thanks.

Rushi Rokad - 4 years, 1 month ago

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