Question

if p/q= 1/2 +1/4+1/8+1/16+1/32+1/64 find p+q​

Answer 1

Solution:-

Add $\dfrac{1}{64}$ on both sides.

$\rightarrow\dfrac{p}{q}+\dfrac{1}{64} =\dfrac{1}{2} +\dfrac{1}{4} +\dfrac{1}{8} +\dfrac{1}{16} +\dfrac{1}{32} +\dfrac{1}{64} +\dfrac{1}{64}$

$\rightarrow\dfrac{p}{q}+\dfrac{1}{64} =\dfrac{1}{2} +\dfrac{1}{4} +\dfrac{1}{8} +\dfrac{1}{16} +\dfrac{1}{32} +\dfrac{1}{32}$

…

$\rightarrow\dfrac{p}{q}+\dfrac{1}{64} =1$

$\rightarrow\dfrac{p}{q}=1-\dfrac{1}{64}$

$\rightarrow\boxed{\dfrac{p}{q} =\dfrac{63}{64} }$

$\therefore p+q=127$