As we are given with [tex] \\\{Log_{2}}^{3}.{Log_{3}}^{4}........{Log_{n+1}}^{n}.{Log_{n+1}}^{2}\\\\ [/tex]
Now using the change of base property ,we can re-write
[tex] \\
=\frac{Log3}{Log2}.\frac{Log4}{Log3}.....\frac{Log(n+1)}{Logn}.\frac{Log2}{Log(n+1)}\\
\\ [/tex]
Each log has base of 10
[tex] \\
=\frac{1}{Log2}.Log2=1\\ [/tex]
