How do you do Gauss summation?

How do you do Gauss summation?

Gauss noticed that if he was to split the numbers into two groups (1 to 50 and 51 to 100), he could add them together vertically to get a sum of 101. Gauss realized then that his final total would be 50(101) = 5050.

What do the numbers 1 through 100 add up to?

The sum of the numbers 1-100 would be equal to the number of pairs (50) multiplied by the sum of each pair (101), or 50 x 101 = 5,050.

What is the formula for summation of 1 2 3 N?

For those of you who are unfamiliar with this series, which has come to be known as the Ramanujan Summation after a famous Indian mathematician named Srinivasa Ramanujan, it states that if you add all the natural numbers, that is 1, 2, 3, 4, and so on, all the way to infinity, you will find that it is equal to -1/12.

What is the Gauss formula?

Gauss added the rows pairwise – each pair adds up to n+1 and there are n pairs, so the sum of the rows is also n\times (n+1). It follows that 2\times (1+2+\ldots +n) = n\times (n+1), from which we obtain the formula. Gauss’ formula is a result of counting a quantity in a clever way.

What is the Gauss theory?

Gauss theorem. Gauss’ theorem tells us that the possible roots of a polynomial are obtained by means of the quotient between the divisors of the independent term and the divisors of the main coefficient (coefficient of the term with the highest degree).

Why is Gauss’s law important?

Gauss’s Law is a general law applying to any closed surface. It is an important tool since it permits the assessment of the amount of enclosed charge by mapping the field on a surface outside the charge distribution. For geometries of sufficient symmetry, it simplifies the calculation of the electric field.

What is the equation for electric flux?

Electric Flux Formula. The electric flux through a planar area is defined as the electric field times the component of the area perpendicular to the field. Electric flux = Electric field * Area * (angle between the planar area and the electric flux) The equation is: Φ = E A cos(θ)