`lim_(n rarr oo){(1+(1)/(n))}^(-n)=`

lim_(n rarr oo)(1-(2)/(n))^(n)

lim_(n rarr oo)((-1)^(n)n)/(n+1)

Evaluate(with the help of definite integral): lim_(n rarr oo){(1+(1)/(n))(1+(2)/(n))dots(1+(n)/(n))}^((1)/(n))

lim_(n rarr oo)(5^((1)/(n))+3^(1/n)-1)^(n)

lim_(n rarr oo)nln( e(1+(1)/(n))^(1-n))

lim_(n rarr oo)(n+(-1)^(n))/(n)

lim_(n rarr oo)(2^(n)+3^(n))^(1/n)

lim_ (n rarr oo) [(1+ (1) / (n)) (1+ (2) / (n)) (1+ (n) / (n))] ^ ((1) / (n) )

Show that lim_(n rarr oo)((1)/(n+1)+(1)/(n+2)+...+(1)/(6n))=log6