Sn(oo) must now be found. From Reference 11, page 177, it is seen that for large u and integer k: where the ± sign refers to even (+) or odd (-) n. Taking the upper bound and changing the variable name from u to a gives: Note that the right side of Equation 30 is independent of n, so this inequality applies to n-1 as well. Thus: Since n = 1, 2, 3, ... , the right side of these inequalities will always have "a" to a positive power in the denominator, and hence, the expressions in Equations 31a and 31b go to 0 as "a" becomes infinite. Applying this limit to Equation 27 gives:
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