Question

The sum can be found of an infinite $G.P.$ whose common ratio is $r$

• A. For all value of $r$
• B. For only positive values of $r$
• C. Only for $0<r<1$
• D. Only for $-1<r<1(r\ne 0)$

Answer 1

The correct option is D

Only for $-1<r<1(r\ne 0)$

Explanation for the correct option

The formula for a geometric progression$=\frac{a}{1-r}$, where $-1<r<1(r\ne 0)$

If $r>1$,then the value of $1-r$ will be negative but this is not possible as $r$ is positive, all the elements of geometric progression will also be positive and their sum cannot be negative.

Hence, option D is correct.