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Here are a few closed formulas for sequences:

• \(a_n = n^2\text{.}\)

• \(\d a_n = \frac{n(n+1)}{2}\text{.}\)

• \(\d a_n = \frac{\left(\frac{1 + \sqrt 5}{2}\right)^n - \left(\frac{1 - \sqrt 5}{2}\right)^{-n}}{\sqrt{5}}\text{.}\)