An infinite G.P. with negative common ratio can have a finite sum only if −1<r<0.
Show that in an infinite G.P. with common ratio r(|r|<1), each term bears a constant ratio to the sum of all terms that follow it.
If s is the sum of an infinite G.P, the first term a then the common ratio r given by
The sum of the infinite G.P. a + a r2 + a r3 . . . . . . a is finite. Then,