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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

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

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

Sum of consecutive (pyramidal) squares

In mathematics, a pyramid number, or square pyramidal number, is a figurate number that represents the number of stacked spheres in a pyramid with a square ... more

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

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

Heronian mean

The Heronian mean of two non-negative real numbers is a weighted mean of their arithmetic and geometric means.The weighted mean is similar to an ... more

Weighted geometric mean

In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the ... more

Resonant frequency of string

Acoustic resonance is the tendency of an acoustic system to absorb more energy when it is forced or driven at a frequency that matches one of its own ... more

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