$$S(n) = 1 + 2 + ... + n = \sum_{i=1}^n{i}$$
$$S(n) = 2 + 4 + ... + 2n = \sum_{i=1}^n{2i}$$
$$S(n) = 1 + 3 + ... + (2n + 1) = \sum_{i=1}^n{(2i + 1)}$$
$$S(n) = \frac{1}{1} + \frac{1}{2} + ... + \frac{1}{n} = \sum_{i=1}^n{\frac{1}{i}}$$
$$S(n) = \frac{1}{2} + \frac{1}{4} + ... + \frac{1}{2n} = \sum_{i=1}^n{\frac{1}{2i}}$$
$$S(n) = \frac{1}{1} + \frac{1}{3} + ... + \frac{1}{2n+1} = \sum_{i=1}^n{\frac{1}{2i+1}}$$
$$P(n) = 1 * 2 * ... * n = n!$$
$$P(x, n) = x * x * .. * x = x^n$$
$$S(n) = 1! + 2! + ... + n! = \sum_{i=1}^n{i!}$$
$$S(n) = x + x^2 + ... + x^2 = \sum_{i=1}^n{x^i}$$
$$S(n) = 2! + 4! + ... + (2n)! = \sum_{i=1}^n{(2i)!}$$
$$S(n) = 1! + 3! + ... + (2n+1)! = \sum_{i=1}^n{(2i+1)!}$$
$$S(n) = \sqrt{2 + \sqrt{2 + ... + \sqrt{2 + \sqrt{2}}}}$$
$$S(n) = \sqrt{1 + \sqrt{2 + ... + \sqrt{n-1 + \sqrt{n}}}}$$
$$S(n) = \sqrt{n + \sqrt{n-1 + ... + \sqrt{2 + \sqrt{1}}}}$$
$$S(n) = 1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{ 1 + \frac{1}{1 + \frac{1}{1 + 1}}}}}$$