Re: Infinite series question

jane schrieb:
Suppose, x_i in R, 0 < x_i < 1, sum_i x_i = oo, and

A_n = sum_{i <= i <= n} x_i, so that A_n -> oo.

B_n = sum_{1 <= i <= n} x_i exp[-A_n * xi].

Are there any known results under which conditions
on (x_i), we have that B_n -> 0 as n -> oo ?

Thanks.

Hi jane,

maybe I overlooked something, but:

B_n >= x_1 exp[-x_1 ^ 2] for all n and therefore no
such sequence x_i
exists.

No, B_n >= x_1 exp[-A_n * x_1], and since A_n > oo, then

this lower bound tends to 0, we probably don't get anything in this way.

Thanks.

Peter
.

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