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Answer either (i) or (ii).
(i) Given that the sequence whose

n

th term is

(s_n + 2s_{n + 1})

converges, show that the sequence

\{ s_n \}

converges also.
(ii) A plane varies so that it includes a cone of constant value equal to

\pi a^3 / 3

with the surface the equation of which in rectangular coordinates is

2xy = z^2.

Find the equation of the envelope of the various positions of this plane.
State the result so that it applies to a general cone (that is, conic surface) of the second order.

Problem Statement