16 SPECIAL TOPICS IN THEORETICAL ARITHMETIC

k=n
According to this notation P, = II (az)
k=1

Ex. 1. I (2) = 2-4:6 - (27)

k=1
Here P; = 2
Pyec2 W4 = 8

Ex. 2. fI (%) = 12.22.32 ... o2
1

Here P; = 12 = 1
P = 1%2.92 = 4
Py = 12.22.32 = 36

Ex.3. II (29 = 22225 ... 27 = 202

1

3

B U8 = (— H(2)12) = — 96

3

Ex.5. II (3k%) = 3
1

41. Sometimes P, can be exprest in terms of n by well
known operations.

Th. Thus for a geometric progression it is easily shown by
mathematical induction that

-Pn = an,,,n(n—l)/?