[tex]a=1* \frac{ 2^{2014}-1 }{2-1} = 2^{2014} -1[/tex]
[tex]b=1* \frac{3^{2014}-1}{3-1} = \frac{ 3^{2014}-1 }{2} [/tex]
[tex] (a+1)^{3} =( 2^{2014}-1+1 )^{3}= 2^{6042} [/tex]
[tex] (2b+1)^{2} =(2* \frac{ 3^{2014-1} }{2}+1 )^{2}= 3^{6042} [/tex]
[tex] 2^{6042} < 3^{6042} => (a+1)^{3} <(2b+1)^{2}[/tex]
