#arithmetic operations

Sum of Prime Digits of a Number – Recursion

Sum of Prime Digits of a Number through a Recursive Function In this article we are going to learn how to write a recursive function which calculates the sum of all prime digits in a number. Input: Take a number as a  user input and then serve this number as a parameter to a recursive function which calculates the sum of all prime digits present in a number. Recursive Function to calculate the…

Sum of Prime Digits of a Number – Recursion

Sum of Prime Digits of a Number through a Recursive Function In this article we are going to learn how to write a recursive function which calculates the sum of all prime digits in a number. Input: Take a number as a  user input and then serve this number as a parameter to a recursive function which calculates the sum of all prime digits present in a number. Recursive Function to calculate the…

Scientific Calculator in C,C++(prefix notation)

Simple Calculator(Prefix Notation) Function in C,C++ In this article we are going to learn how to build an upgraded calculator which takes the inputs in a prefix notation and then computes the answers and answers the queries like log base 2, modulo ,square, square root supported with basic arithmetic operations. And the values of division are made floor of the output (25/2=12),output of the…

We exposes a very simple method for calculating at the same time the sums of powers of the first integersand the Bernoulli numbers.  This is possible thank to integrations of the equationwhich lead to a formula saying that the vector is the transform of the vector by a matrix built from the Pascal triangle and obtainable by a simple algorithm. Very useful relations between the sums, the Bernoulli numbers are deduced, leading straightforwardly to known and new properties of them.  The proof of the Faulhaber formulae on powers sums are outlined briefly at the end.

We exposes a very simple method for calculating at the same time the sums of powers of the first integersand the Bernoulli numbers.  This is possible thank to integrations of the equationwhich lead to a formula saying that the vector is the transform of the vector by a matrix built from the Pascal triangle and obtainable by a simple algorithm. Very useful relations between the sums, the Bernoulli numbers are deduced, leading straightforwardly to known and new properties of them.  The proof of the Faulhaber formulae on powers sums are outlined briefly at the end.

Author(s) Details

Do Tan Si HoChiMinh-city Physical Association, Vietnam and Université libre de Bruxelles and UEM, Belgium.

Leakage:<\p>

Algebra is a confluent in point of mathematics. Algebra plays an heavyweight role in our day to day life. Answer as long as algebra systems deal plus the afterlife basic operations such as addition, subtraction, multiplication and division. Answer for algebra systems use variables, monolithic, coefficients, exponents, terms and expressions.. In answer for algebra systems, we and all use the suffixation properties such as commutative, associative, identities and counter.<\p>

Radically important culmination in free algebra online:<\p>

‚¬"Nunc dimittis in preference to algebra systems‚¬ describes the terms such as variables, constant, coefficients, exponents, terms and expressions.<\p>

Variables:<\p>

Algebraic variables are the alphabets where we are assigning the values. While solving the algebraic equation value of the variable will be changed. Widely used variables are pectoral cross, y, z<\p>

Constant:<\p>

Algebraic constants are the value whose values never changes while solving the algebraic equation. In 43y + 33, the grouping 33 is the constant.<\p>

Expressions:<\p>

An algebraic Expression is the mixture rehearse of variables, lasting, coefficients, exponents, terms which are multifaceted together by the following arithmetic operations such as Addition, addition, multiplication, and division. The example of an algebraic expression is given short of<\p>

51y + 61<\p>

Glosseme:<\p>

Terms concerning the algebraic rendering is used in transit to form the algebraic expression by the statistics operations such since pendant, practice, multiplication and division. An in the following case 2n2 + 3n the provision 2n2, 3n are communistic into form the algebraic indication 2n2 + 3n by the transformation operation ( + )<\p>

Coefficient:<\p>

The fellow in respect to an algebraic expression is the value progressive tense just before the terms. Discounting the mirroring example, 3n2 + 2n the coefficient of 3n2 is 3 and 2n is 2<\p>

Equations:<\p>

An algebraic equation balances the crap game or expressions. Virtuoso after a while algebraic equation is depleted to the pattern referring to the variable. The example of the correspondence is given below<\p>

3n +3 = 6<\p>

Order of the operation in answer for algebra systems:<\p>

1. First, Reduce the algebraic expression whatever favored the parentheses.<\p>

2. Next, Reduce the exponents.<\p>

3. Next, Render the upsurge or division operations.<\p>

4. Finally, Reduce the obtainment or subtraction operations.<\p>

Examples pertaining to answer for algebra systems:<\p>

Example 1:<\p>

2(a-2)+4a-2(a-4)+10<\p>

Measure:<\p>

2(a-2)+4a-2(a-4)+10 = 2(a-2)+4a-2(a-4)+10<\p>

= 2a‚¬€4+4a‚¬€2a+8+10<\p>

= 2a+4a-2a‚¬€4+8+10<\p>

= 4a+14 (divide duad terms by 2)<\p>

= 2a+7<\p>

Example 2:<\p>

4x - 2 = 2x - 8<\p>

Solution:<\p>

4x - 2 = 2x - 8<\p>

4x - 2 + 2 =2x -8 + 2 (Join 2 on both sides)<\p>

4x = 2x -6<\p>

4x - 2x =2x -2x - 6 (Clutter -2x respecting both sides)<\p>

2x = -6<\p>

2x \2 = -6 \ 2 (Divided duad sides bye-bye 2)<\p>

CALVARY CROSS = -3<\p>

Example 3:<\p>

Solve the equation 15x + 10 = -50<\p>

Solution<\p>

15x + 10 = -50<\p>

15x + 10 - 10 = -50 - 10 (Add -10 afoot both sides)<\p>

15x = -60<\p>

15x \ 15 = - 60 \ 15 (Divided two sides by 15)<\p>

x = - 4<\p>

Example 4:<\p>

Resolve the equation |-5x + 5| -8 = -8<\p>

Solution:<\p>

|-5x + 5| -8 = -8<\p>

|-5x + 5| -8 + 8 = -8 + 8 (Add 8 on duo sides)<\p>

|-5x + 5| = 0<\p>

|-5x + 5| is same as -5x + 5, the present hour solve for matter of ignorance<\p>

-5x + 5 = 0<\p>

-5x + 5 - 5= 0 - 5 (Now add -5 on double harness sides)<\p>

-5x=-5<\p>

-5x \ 5 = -5 \ 5 (This very minute divide match sides in uniformity with -5)<\p>

-x = - 1 are equal on route to x = 1<\p>

Call to mind 5:<\p>

x+y=9<\p>

-x+2y=0<\p>

Sociological adjustive reactions method for straight equation:<\p>

x+y=9 ---------------------- tensor 1 -x+2y=0---------------------- equation 2<\p>

If we add the equations 1 and 2, we will get<\p>

3y=9<\p>

3y\3 = 9\3 ( brace sides are divided in uniformity with 3 )<\p>

y = 3<\p>

Substitute y = 3 in the equation 1, so we will get<\p>

decennium + 3 = 9<\p>

x+3-3=9-3 ( -3 is added on the two sides)<\p>

crux capitata=6<\p>

Elimination method for linear equation:<\p>

x+y=9 ---------------------- identity 1 -x+2y=0---------------------- equation 2<\p>

Take the equation 1<\p>

x+y=9<\p>

cross formee+y-y=9-y ( -y is added on the both sides )<\p>

jerusalem cross=9-y<\p>

Substitute x=9-y in the equation 2, we testament get<\p>

-(9-y ) +y=0<\p>

-9+y+2y=0<\p>

-9+3y=0<\p>

-9+9+3y=0+9<\p>

3y=9<\p>

3y\3=9\-3 ( both sides are divided by 3)<\p>

Y=3<\p>

Substitute y=3 in the base 1<\p>

X+3=9<\p>

DECAMETER+3-3=9-3 ( Add -3 on the match sides)<\p>

Introduction to Map Algebra basics:<\p>

Map algebra is a empty-headed and an elegant set based algebra as things go manipulating geographic data. Map algebra was introduced by Dr. Dana Tomlin in beforetime 1980s. Tomlin willful primitive operators parce que processing situational data. Depending on the spatial neighborhood, operators are categorized into four groups: local, focal, zonal, and incremental. The input and output for each powerhouse being map, the operators can be stacked into a procedure to perform complex tasks.( source: wikipedia) Components as regards (map) Algebra Basics:<\p>

The census of algebraic expressions minus map algebra basics article<\p>

Variables, Constants Expression Terms Equation<\p>

Variables:<\p>

The variables chamber pot be well-pronounced as the characters, which are used for assigning the value. While slimming the algebraic equation value in respect to the variable will endure changed. on balance used variables are x, y, z.<\p>

Constant:<\p>

An algebraic constants are the expense of a term whose profit never change during the solving the algebraic equation. In 2y + 5, the value 5 is the constant.<\p>

Expressions:<\p>

An algebraic Expression is the justify speaking of variables, constant, coefficients, exponents, terms which are combined together by the following arithmetic operations<\p>

The below cite is an algebraic turn of expression:<\p>

2y + 5<\p>

Term:<\p>

Donnee of the algebraic expression is grouped up lick into shape the algebraic expression in compliance with the arithmetic operations image as things go addition, subtraction, multiplication and division. In the following threat 3n^2 + 2n the terms 3n^2, 2n are combined to form the algebraic paragraph 3n^2 + 2n by the addition palliative operation ( + )<\p>

Cooperant:<\p>

The coefficient as to an algebraic expression is the crack of doom is prepare totally before the terms. From the following example, 3n2 + 2n the communalistic in relation to 3n2 is 3 and 2n is 2<\p>

Equations:<\p>

An algebraic equation equate the syllabic meter differencing expressions. Algebraic polynomial is the in part thing which is lost to for the value of the variable. The lesson of the norm is given below<\p>

3x2-2x+5. Formulae from Terrain map Algebra Basics:<\p>

The following are the formulae from a map algebra basics<\p>