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If $I_n = \int_0^{\pi/2} \cot^n x,dx$, then:
(1) $\dfrac{1}{I_2 + I_4}, \dfrac{1}{I_3 + I_5}, \dfrac{1}{I_4 + I_6}$ are in G.P.
(2) $\dfrac{1}{I_2 + I_4}, \dfrac{1}{I_3 + I_5}, \dfrac{1}{I_4 + I_6}$ are in A.P.
(3) $I_2 + I_4, I_3 + I_5, I_4 + I_6$ are in A.P.
(4) $I_2 + I_4, (I_3 + I_5)^2, I_4 + I_6$ are in G.P.
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