Question

Al simplificar el producto:
[1 + $\frac{1}{3}$ ][1 + $\frac{1}{4}$ ][1 + $\frac{1}{5}$ ][1 + $\frac{1}{6}$ ]...[1 + $\frac{1}{n}$]

Answer 1

Tienes lo siguiente:
$1+ \frac{1}{3}= \frac{3}{3}+ \frac{1}{3}= \frac{4}{3} \\\\1+ \frac{1}{4}= \frac{4}{4}+ \frac{1}{4}= \frac{5}{4} \\ \\ 1+ \frac{1}{5}= \frac{5}{5}+ \frac{1}{5}= \frac{6}{5} \\.\\.\\. \\ 1+ \frac{1}{n}= \frac{n}{n}+ \frac{1}{n}= \frac{n+1}{n} \\ \\ (1+ \frac{1}{3} )(1+ \frac{1}{4} )(1+ \frac{1}{5} )...(1+ \frac{1}{n} )=( \frac{4}{3} )( \frac{5}{4} )( \frac{6}{5} )...( \frac{n+1}{n} )= \boxed{\frac{n+1}{3}}$

Saludos!