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10 results for “sequence”

Formulae (10)

S_n = \frac{n}{2}(a_1 + a_n)

Sum of the first n terms of an arithmetic sequence.

a_n = a_1 + (n-1)d

The nth term of an arithmetic sequence.

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-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.

C_n = \frac{1}{n+1}\binom{2n}{n}

Counts many recursive structures such as balanced parentheses.

\frac{L}{L_\odot} \approx \left(\frac{M}{M_\odot}\right)^{3.5}

How a main-sequence star's brightness scales with its mass.

T_n = \frac{n(n+1)}{2}

Sum of the first n natural numbers.

F_n = F_{n-1} + F_{n-2}

Each term is the sum of the two before it.

F_n = \frac{\varphi^n - \psi^n}{\sqrt{5}}

Closed form for the nth Fibonacci number.