Assume that # 1a_1+2a_2+\cdots+na_n=1, # where the #a_j# are real numbers. As a function of #n#, what is the minimum value of #1a_1^2+2a_2^2+\cdots+na_n^2?#
1 Answer
May 21, 2017
Explanation:
The Lagrangian reads
The stationary conditions
and
so
so the minimum value is given by