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[VA] SRC#005- April, 1st Mean Minichallenge
04-07-2019, 12:01 AM (This post was last modified: 04-07-2019 12:09 AM by Albert Chan.)
Post: #7
RE: [VA] SRC#005- April, 1st Mean Minichallenge
Hi, Maximilian:

I too were afraid of posting a "stupid" solution (never heard of Generalized Mean)

Mk^k = (a1^k + ... + an^k) / n

The case for k=0 doesn't fit quite right, getting meaningless result, M0 = 1^∞
I had to convince myself this work for Geometric Mean.

For k=ε (small value, but not exactly 0):

LHS = Mε^ε = e^(ε ln(Mε)) ≈ 1 + ε ln(Mε)

RHS = (a1^ε + ... + an^ε) / n ≈ ((1 + ε ln(a1)) + ... + (1 + ε ln(an))) / n ≈ 1 + ε ln(a1 ... an) / n

⇒ Mεn√(a1 ... an)
⇒ M0 = n√(a1 ... an)
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RE: [VA] SRC#005- April, 1st Mean Minichallenge - Albert Chan - 04-07-2019 12:01 AM



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