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Calculus Level 3

∑ n = 0 ∞ ( − 1 ) n 2 n + 1 \large\sum_{n=0}^\infty\frac{(-1)^n}{2n+1}

If the value of the series above can be expressed as a π b \dfrac{a\pi}b for coprime positive integers a a and b b , find the minimum nonzero positive value of a + b a+b .


The answer is 5.

Alisyr Khalil by alisyr khalil , 32, Syria

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1 solution

Jafar Badour
Oct 24, 2015

∑ i = 0 ∞ ( − 1 ) n ( 2 n + 1 ) = 1 4 ( − 1 ) m f ( 0 ) ( 1 2 ( m + 5 2 ) ) − 1 2 ( m + 3 2 ) ) ) + p i 4 \displaystyle \sum_{i=0}^\infty \frac{ (-1)^n}{(2 n+1)} = \frac{1}{4} (-1)^m f^{(0)} (\frac{1}{2} (m+\frac{5}{2}))-\frac{1}{2} (m+\frac{3}{2})))+\frac{pi}{4}

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not understood

alisyr khalil - 5 years, 7 months ago

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