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Calculus Level 4

∑ x = 0 ∞ ∫ 0 x cos ⁡ 29 ( π θ ) d θ = ? \large \sum_{x=0}^\infty \int_0^{x} \cos^{29} (\pi\theta) d \theta = \ ?

− ∞ -\infty ∞ \infty 1 π 4 / 2 π^{4}/2 0

Akira Kato by Akira Kato , 22, China

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1 solution

Akira Kato
Jul 13, 2016

After taking integral, all the terms have s i n ( n π θ ) sin(n\pi\theta) so the sum is 0.

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