Some Useful Formulae

In science, a formula, such as a mathematical formula or a chemical formula, is a brief way to convey information symbolically. The basic concept of a connection between specified quantities is referred to as a formula in informal science use.

Formulas, which derives from the most prevalent plural noun form in English, or formulae, which is influenced by scientific Latin (from the original Latin)

A short note on Some Useful Formulae

A formula in mathematics is typically an identity that compares one mathematical statement to another, with mathematical theorems being the most significant examples. A formula, often known as a “well-formed formula,” is a construct made utilising the symbols and construction guidelines of a particular logical language. For instance, calculating the volume of a sphere needs a large amount of integral calculus or the method of exhaustion, which is its geometric equivalent. However, mathematicians have developed a formula to express the volume of a sphere in terms of its radius after having done this once in terms of some parameter (the radius, for example)

Once this conclusion has been established, any sphere’s volume may be calculated provided that it is known what its radius is. It is important to note that the volume V and the radius r are written as single letters in this example rather than sentences or phrases. This practice allows mathematicians to handle bigger, more complicated formulae more rapidly, even if it is less significant in relatively basic formulas. Algebraic, analytical, or closed form formulae are often used in mathematics.

The common ratio of the geometric series

The distance between each number in a geometric series is known as the common ratio. The reason it is common to all numbers and also the ratio between two successive numbers in the sequence is why it is known as the common ratio.

Simply divide each number in the series by the number before it to find the common ratio. What, for instance, is the common ratio in the list of integers below?

{2, 4, 8, 16}.

Divide each number in the series by the one that comes before it, starting with the number at the end.

16 / 8 = 2.

Divide again to make sure that each number in the series follows the same pattern.

8 / 4 = 2.

4 / 2 = 2.

You may say that the common ratio is 2, as it is the same for each group.

As a result, the following is the formula to determine a geometric sequence’s common ratio:

d = a(n) / a (n – 1).

Where the final phrase in the series is a(n), and the term before that is an-1.

If you split the series and discover that each number’s ratio is different, there is no common ratio and the sequence is not geometric.

Some Useful mathematical equations

The Basel Problem

According to this equation, pi squared over six is obtained by taking the reciprocal of each square integer and adding it to itself. Euler demonstrated this. Keep in mind that Equation 2 (the Euler product formula) from earlier in this post’s left side is all that this sum is, with s equal to2. The Riemann zeta function is represented by that equation, and we may define zeta of 2 as pi squared times six.

1+1 / 4+1 / 9+1 / 16+1 / 25+…=π² / 6

A series of harmonics

It implies that even if you add a large number of decreasing integers (which eventually become zero), they will still reach infinity, which is counterintuitive. The sum of all the squared numbers, however, does not equal infinity (it adds up to pi squared over six). If you pay close attention, the harmonic series is just zeta of1.

1+1 / 2+1 / 3+1 / 4+1 / 5+…=∞

Useful excel formulas

A formula in Microsoft Excel is an expression that modifies values in a set of cells. Even if the result is incorrect, these formulae nonetheless yield a result. You may execute calculations like addition, subtraction, multiplication, and division using Excel formulae. Excel also allows you to work with date and time information, discover averages and percentages for a range of cells, and perform a lot more things.

AVERAGE, COUNT, AND SUM. By choosing them or entering them in, you may use SUM to add up any number of columns or rows. For instance, =SUM(A1:A8) would add up all values between A1 and A8, and so on.

STATEMENTS OF IF

COUNTIF, SUMIF, and AVERAGEIF

Conclusion 

The Riemann zeta function is represented by that equation, and we may define zeta of 2 as pi squared times six. Excel also allows you to work with date and time information, discover averages and percentages for a range of cells, and perform a lot more things. . The reason it is common to all numbers and also the ratio between two successive numbers in the sequence is why it is known as the common ratio.