" (iii) "lim_(n rarr oo)[(1+(1)/(n))(1+(2)/(n))(1+(3)/(n))cdots(1+(n)/(n))]^((1)/(n))

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

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

" (e) "lim_(n rarr oo)[(n!)/(n^(n))]^(1/n)

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

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

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