If S be the sum,P be the product and R the sum of reciprocals of n terms in a G.P,prove that P2=(SR)n?

1 Answer
Mar 16, 2018

See below.

Explanation:

The right formulation is

P2=(SR)n+1

because

S=nk=0ak=an+11a1

R=nk=0ak=1an+111a1=a(1an+1)(1a)an+1

then

SR=an

and

P=nk=0ak=ank=0k=an(n+1)2

hence

P2=an(n+1)an×n

so the exact formulation is

P2=(SR)n+1