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Let a1,a2,...,an be real numbers such that a21+2a22++na2n=1.
Find the maximum value of (a1+2a2++nan)2, in terms of n

 

I originally got the answer of 1 but it was wrong! Thanks for helping!

 Mar 2, 2025
 #1
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See my previous answer to your a12 question. It should be a similar (if not the exact same) process with Cauchy Schwarz. 

 

Edit: my previous answer got large ai language modeled. 

 

Here is how to start with cauchy: xi=i20i=1xi=1+2+...+2020i=1x2i=1+2+...+20. Cauchy says sum of x^2 * sum of y^2 >= sum of (xy)^2. 

 Mar 2, 2025
edited by Kromy  Mar 2, 2025

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