[tex]a) (n+1)(n+2)=n^{2} +3n+2\\n^{2} +2n+n+2=n^{2} +3n+2\\n^{2} +3n+2=n^{2} +3n+2 (q.e.d.)\\\\b) \frac{1}{3}+\frac{n}{2} +\frac{n^{2} }{6}=\frac{2+3n+n^{2} }6 \\\\n=1 => 2+3+1/6=6/6=1\\n=2=>2+6+4/6=12/6=2\\n=4=>2+12+16/6=30/6=5\\n=5=>2+15+25/6=42/6=7\\...[/tex]
