Recursively, we also know that T(n)=T(n1)n Manipulating this formula a bit, we can see that T(n1)=T(n)n We can then substitute this value into our first equation to see that T(n)nT(n)=n2 Combining some like terms, we see that 2T(n)n=n2 Again, using some algebraic manipulation, we could arrive at T(n)=n(n1)/2, where T(n) is equal to the sum of the first n natural numbers Our notation and the second introduces you to the Sigma notation which makes the proof more precise A visual proof that 123n = n (n1)/2 We can visualize the sum 123n as a triangle of dots Numbers which have such a pattern of dots are called Triangle (or triangular) numbers, written T (n), the sum of the integers from 1 to nUsw auch wenn etwas gekürzt wird in einer Rechenaufgabe verstehe ich nie warum und wieso, vor allem wie zb (n4)! Arithmetic Progression Wikipedia N(n+1)/2 formula name
