[VA] SRC #012c - Then and Now: Sum

[J-F Garnier]

(12-04-2022 10:16 AM)Albert Chan Wrote:  Both are exactly the same, except mine start from 1, yours start from M ≠ 1
If we re-define sum = index from M to K-1, we have:

(S-S1)*(1-LN2) ≥ sum((G-LN2)/F) = S2

(12-03-2022 12:15 PM)Albert Chan Wrote:  S = sum(G/F) + LN2 * SUM(G/LN2/F)

Since G/LN2 ≥ 1, no matter how big K is, we have:

S ≥ sum(G/F) + LN2 * SUM(1/F)
S ≥ sum(G/F) + LN2 * (S - sum(1/F))

S*(1-LN2) ≥ sum((G-LN2)/F)

No need to hard code conditions for index K, or for G converged to LN2.
Just sum RHS until convergence. It will converge, very quickly.

What I don't understand in your reasoning is how you moved from:
S*(1-LN2) ≥ sum((G-LN2)/F)
to
S*(1-LN2) = sum((G-LN2)/F) when the sum has converged.

J-F
(not a mathematician)