Question

Answer 1

\(\dfrac{1}{2}>\dfrac{1}{3}\) ; \(\dfrac{1}{2^2}>\dfrac{1}{3^2}\) ; ....; \(\dfrac{1}{2^{100}}>\dfrac{1}{3^{100}}\)

\(\Rightarrow1+\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{100}}>1+\dfrac{1}{3}+\dfrac{1}{3^2}+...+\dfrac{1}{3^{100}}\)

\(\Rightarrow B>A\)