Question

For how many real values of '$p$' infinity sum of $p,1,\frac{1}{p},......$ is $\frac{25}{4}$.

Answer 1

For $\infty$ G.P. sum

$S_{\infty }=\frac{a}{1-r}$ i here $a=b$

& $r=\frac{1}{p}$

$\Rightarrow \frac{P}{(1-\frac{1}{p})}=\frac{25}{4}$

$\Rightarrow p^2=\frac{25}{4}(p-1)$

$\Rightarrow 4p^2-25p+25=0$

As $p=225>0$

${\therefore }^{\prime }{2}^{\prime }$ real value.