Conversion Rule: lim(n->infinity) (1/n) * sum(r=1 to n) f(r/n) = integral(0 to 1) f(x) dx

Steps:

1. Write the sum as (1/n) * sum f(r/n)
2. Replace r/n by x and 1/n by dx
3. Limits: when r starts at 1 (or 0), x = 0; when r = n, x = 1
4. Evaluate the definite integral

General form: lim(1/n) * sum(r=p to q) f(r/n) = integral(p/n to q/n) ... but with n->inf, lower limit = lim(p/n), upper = lim(q/n).

Example: lim [1/(n+1) + 1/(n+2) + ... + 1/(3n)] = lim (1/n) sum(r=1 to 2n) 1/(1+r/n) = integral(0 to 2) dx/(1+x) = ln 3.