|   1       0     0   0  . .. |          |    b  1   1   1 .. |
 C=|   a       1     0   0   …|  ,  A=|     1  b   1  1   ..|
     |   a^2    a     1   0   …|          |     1  1   b  1  … |
     |   a^3    a^2  a   1   …|          |    1  1   1  b   .. |
        ..        ..    ..   … . ..               .. …  …  …

           Let define as M=C’ACC’AC.
         My problem is to find the asymptotic behaviour of
         trace(M) which is eqaul to sum((i=1 to n)(j=1 to n)(Mij^2))
as n increases. I tested this in matlab.It is O(n^2). But I can’t
derive it anatically. It seemed to me very complicated. Can someone
help please? Thanks.

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>        sum(a^i* (n^2-i^2)),  i=n, n+1, …..,n   for |a|<1

>       here sum refers the sigma notation. Thanks alot.

As the sum is on i and it goes from n to … n, there is but
one term in the sum, namely when i = n.  Thus
        sum(…) = a^n (n^2 – n^2) = 0

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