Another formula you may have seen before is

One way to prove this is to let *S* be the sum. Then

Subtracting them yields

You might recognize this formula in another guise. Change *n*+1 to
*n* and multiply both sides by 1-*r* to get

Some special cases of this are when *n*=2,3,4:

You should recognize these as special cases of some formulas you learned when factoring polynomials.

Wed Apr 21 08:17:28 EDT 1999