If n is a positive integer, then 1 + 2 + 3 + ⋯ + n has order__________.

To find:

The order of 1+2+3+...+n where n is a positive integer.

Formula used:

Let f and g be real valued functions defined on the same nonnegative integers, with g(n)≥0 for every integer n≥r, where r is positive real number.

Then,

f is of order g, written f(n) is Θ(g(n)), if and only if, there exist positive real numbers A,B and k≥r such that

Ag(n)≤f(n)≤Bg(n) for every integer k≥a.

The summation of first n terms of an arithmetic progression is given by

Sn=n2(a+l)

Where, n= number of termsa= first terml= last termSn= simmation of n terms.

Calculation:

The given series 1+2+3+