Question

Tot la ajutorul vostru apelez. Multumesc! ​

Answer 1

 

$\displaystyle\bf\\\frac{1}{2^3}+\frac{1}{2^2\cdot3}+\frac{1}{2\cdot3^2}+\frac{1}{3^3}=\\\\\\=\frac{^{3^3)}1}{2^3}+\frac{^{2\cdot3^2)}1}{2^2\cdot3}+\frac{^{2^2\cdot3)}1}{2\cdot3^2}+\frac{^{2^3)}1}{3^3}=\\\\\\=\frac{3^3}{2^3\cdot3^3}+\frac{2\cdot3^2}{2^3\cdot3^3}+\frac{2^2\cdot3}{2^3\cdot3^3}+\frac{2^3}{2^3\cdot3^3}=\\\\\\=\frac{3^3+2\cdot3^2+2^2\cdot3+2^3}{2^3\cdot3^3}=\\\\\\=\frac{27+18+12+8}{8\cdot27}=\boxed{\bf\frac{65}{216}}$