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Geometric progression (nth term)

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous ... more

Wiswesser's rule

The Wiswesser rule gives a simple method to determine the energetic sequence of the atomic subshells (n,l). n is the principal quantum number and l is the ... more

Arithmetic progression

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant and is ... more

Triangular number

A triangular number or triangle number counts the objects that can form an equilateral triangle. The nth triangle number is the number of dots composing a ... more

Sum of consecutive (triangular) cubes (Nicomachus's theorem)

In number theory, the sum of the first n cubes is the square of the nth triangular number. The sequence of squared triangular numbers is

0, 1, 9, ... more

Standard deviation of any arithmetic progression

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant and is ... more

Sum of natural numbers raised to the fifth power

he formula is a special case of general Faulhaber’s formula and gives the sum of natural consecutive numbers raised to the fifth power,(starting with 1), ... more

Geometric series (sum of the numbers)

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous ... more

Permutation ( k-permutations of n)

Informally, a permutation of a set of objects is an arrangement of those objects into a particular order. The notion of permutation relates to the act of ... more

Sum of the infinite terms

A geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous ... more

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