The formal theory of a given infinite series does not require a numerical value as the sum assigned to it. However, to make a distinction between divergent and convergent series, it is necessary to obtain certain formulas for the nth partial sum. For example, the infinite series: 1/(1x2)+1/(2x3)+1/(3x4)+1/(4x5)+…+1/n(n+1)+…has partial sums S(1)=1/2, S(2)=1/2+1/6=2/3, S(3)=1/2+1/6+1/12=3/4, and S(n)=n/(n+1). This formula is derived from the telescoping series given by S(n)=(1-1/2)+(1/2-1/3)+(1/3-1/4)+…+(1/(n)-1/(n+1)) where all inner terms cancel and only the begin and end terms remain such that 1-1/(n+1)=n/(n+1). Since this formula is a particular rational function, it can be said that this particular infinite series has been rationalized. Furthermore, it can be determined that the limit exists if and only if 1/(infinity+1)=0. This limit is identically unity.