Who invented the formula N N 1 2?

Who invented the formula N N 1 2?

Carl Friedrich Gauss
The German mathematician and scientist, Carl Friedrich Gauss, is said to have found this relationship in his early youth, by multiplying n2 pairs of numbers in the sum by the values of each pair n + 1.

What is the formula n n 1 )/ 2 for?

The formula n(n−1)/2 for the number of pairs you can form from an n element set has many derivations, even many on this site. One is to imagine a room with n people, each of whom shakes hands with everyone else. If you focus on just one person you see that she participates in n−1 handshakes.

How did Carl Friedrich Gauss found the sum of the first 100 counting numbers?

What is the sum of the first 100 whole numbers? 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 is the sum of first four odd natural numbers?

Sum of first four odd numbers = 1 + 3 + 5 + 7 = 16.

How do you prove P(N)?

The technique involves three steps to prove a statement, P (n), as stated below: Verify if the statement is true for trivial cases like n = a i.e. P (a) is true. [Base Case] Assume that the statement is true for n = k for some k ≥ a i.e. P (k) is true. [Inductive Hypothesis]

Is -is an identity for n = k+1?

Therefore the result is also true for n = k+ 1. Hence by the principle of mathematical induction, the result is true for all i.e., -is an identity. Noticing that the sum on the left telescopes and distributing the sum over the two terms on the right, we finally have: i.e., -is an identity. 8 clever moves when you have $1,000 in the bank.

Is a k = a 1 + (k – 1) true for all?

Let us assume that the formula a k = a 1 + (k – 1) is true for all natural numbers. a k + 1 = a 1 + [ (k + 1) – 1] d = a 1 + k · d. Thus the formula is true for k + 1, whenever it is true for k. And we initially showed that the formula is true for n = 1. Thus the formula is true for all natural numbers.

Is the sum of -th powers of first natural numbers a polynomial?

If is a natural number than the sum of -th powers of the first natural numbers is a polynominal in variable of degre and with rational coefficients (Wikipedia calls them Faulhaber polynomials, see Faulhaber’s formula – Wikipedia ):