Usuario:Pino/analisis

$0<{\sqrt {(n+1)}}-{\sqrt {n}}<{\sqrt {(n+1)}}$

$0<({\sqrt {(n+1)}}-{\sqrt {n}})({\sqrt {n+1}}+{\sqrt {n}})<{\sqrt {n+1}}({\sqrt {n+1}}+{\sqrt {n}})$

$0<1<n+1+(n+1)^{1/2}$

$0<1/(n^{1/2})<{\frac {n+1+(n(n+1))^{1/2}}{(n^{1/2})}}<n+1+(n(n+1))^{1/2}$

$n^{1/2}-(n+1)^{1/2}<n<n+1<n+1+((n+1)n)^{1/2}$

$1/(n)^{1/2}<(n+1+((n+1)n)^{1/2})/(n^{1/2})$

$1/(n)^{1/2}\leq {\frac {(n)^{1/2}-(n+1)^{1/2}}{n^{1/2}}}<{\frac {(n+1+((n+1)n)^{1/2})}{n^{1/2}}}$

$1/(n)^{1/2}<2((n)^{1/2}-(n+1)^{1/2})$