Sums arise often in the study of computer algorithms. For example, if the *i*th iteration of a loop takes time *f*(*i*) and it loops *n* times, then the total time is *f*(1) + *f*(2) + *f*(3) + · · · + *f*(*n*). This we denote as . It can be approximated by the integral , because the first is the area under the stairs of height *f*(*i*) and the second under the curve *f*(*x*). (In fact, both ∑ (from the Greek letter sigma) and *∫* (from the ...

Start Free Trial

No credit card required