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Prove z•=o c(n, k) 2 = c(2n, n). (a) prove the identity using the fact that (1 x) 2n = (1 x)(1 x)n.

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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.

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