Does anyone know why the infinite product of (2 * 3 * 5 * 7 * 11 * 13
* ...) / (1 * 2 * 4 * 6 * 10 * 12 * ...) shouldn't be zero? The book I
was reading this in says it's infinite. Each of the numerators are the
primes, and each of the denominator factors are (prime - 1). I just
thought that I could ignore the 1 in the denominator and the 2's would
cancel leaving (3 * 5 * 7 * 11 * 13 * ...) / (4 * 6 * 10 * 12 * 16
* ...) which is a product that is composed of a series of fractions
all less than 1 (ie 3/4, then 5/6 then 7/10 then 11/12, then 13/16,
etc). Where am going wrong? By the way this product is equivalent to
the harmonic series of Sum (from n=1 to infinity) of 1/n which I
believe is infinity.
Thanks...
-Bob
