Final answer:
The task was to prove a mathematical identity related to binomial coefficients and series expansions, but due to unclear information and potential typos, a precise proof cannot be provided.
Step-by-step explanation:
The question asks to prove the identity z•=o c(n, k) 2 = c(2n, n) using the binomial theorem and manipulations of series expansions. The binomial theorem states that the expansion of (a + b)^n includes terms of the form c(n, k) a^(n-k) b^k where c(n, k) is the binomial coefficient. To demonstrate the identity, we could expand (1 + x)^2n and manipulate the resulting series, but the information provided is unclear and seems to contain typos that prevent an accurate proof.