26. Let a =(a₁,a2,a3,...,an) be an n-tuple of positive real num-bers and (w₁,w2,w3,...,wn) be another n-tuple of positive real numbers (calledweights). Define the weighted mean of order r by1/rM₁(a) =Σ=1 w;a;nΣj=1 Wj(I_17)j=1(1/Σ₁ ₁²₁)if r ‡ 0, and \r\ <∞,if r = 0,if r = -∞,if r = ∞min {a1,92,93,...,an},max {a1,02,03,...,α₂},Suppose r, s are two real numbers such that r < s. Prove thatM-∞(a) ≤ Mr(a) ≤ M₁(a) ≤ M∞(a).

Answered: Image /qna-images/answer/5657cbea-aa7d-402e-8f2d-b28849ec1bc7.jpg

Answered: 26. Let a = (a₁,a2,a3,...,an) be an…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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26. Let a = (a₁,a2,a3,...,an) be an n-tuple of positiv ■d (w₁,w2,W3,..., Wn, ‚wn) be another n-tuple of positive real num =). Define the weighted mean of order r by 1/r Σ;=1 w;a; if r 9. and Irl<