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Question: how to evaluate faster?

Question:how to evaluate faster?

Scimann 511 Maple
January 22 2008
0
I need to evaluate expression

sum((sum((sum((1-p)^i/(a[1]*i+a[1]+a[2]*j+a[2]+a[3]*k+a[3]), i = 0 .. infinity))*(1-p)^j, j = 0 .. infinity))*(1-p)^k, k = 0 .. infinity).

A straightforward evalf(subs(a[1] = .4, a[2] = .1, a[3] = .5, p = 1/3, %)) is too too slow. Are there any faster solutions? Thanks in advance.

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