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7 results for “geometric”

Formulae (7)

S_n = a_1 \frac{1 - r^n}{1 - r}

Sum of the first n terms of a geometric sequence (r ≠ 1).

S = \frac{a_1}{1 - r}, \quad |r| < 1

Sum of an infinite geometric series that converges.

GM = \sqrt[n]{x_1 x_2 \cdots x_n}

The nth root of the product of n numbers.

S = \frac{a}{1-r}, \; |r|<1

Sum of an infinite geometric series that converges.

S_n = a\frac{1-r^n}{1-r}

Sum of the first n terms of a geometric series.

GM = \sqrt[n]{x_1 x_2 \cdots x_n}

The nth root of the product of n values.

P(X=k) = (1-p)^{k-1} p

Probability that the first success occurs on trial k.