Proof Without Words: Limit of a Recursive Root Mean Square

摘要

Visual proof that the limit of the recursive root mean square sequence defined by a_(n+1) = (a_n~2+a_(n-1)~2)/2~(1/2) is (a_1~2+2a_2~2)/3~(1/2) where a_1 and a_2 are the initial values of the sequence.