Mathematics

Problem

Let

S(p)=\displaystyle \sum_{n=1}^{\infty} \left(\dfrac{p}{2}\right)^{n}

and

T=\displaystyle \sum_{n=1}^{\infty} \left(\dfrac{3}{4}\right)^{n}

. For which values of the real parameter

p

does

S(p)

converge and have a sum greater than

T

? a)

0<p<\dfrac{3}{2}

p>\dfrac{3}{2}

\dfrac{3}{2}<p<2

-2<p<\dfrac{3}{2}