Final answer:
The formulas for the entries of a binomial expansion of (a + b)^n involve the binomial theorem and series expansions, using binomial coefficients and powers of a and b.
Step-by-step explanation:
The question seems to be asking to find formulas for the entries of an unspecified mathematical object, given that n is a positive integer. There seems to be a missing part in the question as to what object's entries are to be found. Assuming that the question is about the binomial theorem expansion of a binomial expression, the formula would be:
(a + b)n = an + n an-1b + ··· + bn
where series expansions are used to express (a + b)n. Each term in the expansion can be written as:
with C(n, k) being the binomial coefficient calculated as:
C(n, k) = n! / (k! * (n - k)!).
Each term in the series results from the application of this theorem, which involves combinations of the terms a and b raised to the appropriate powers, reflecting the number of ways to choose a subset of k items from n distinct items.