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Answer 1 · 2018-03-17T05:04:29

The sequence #{(root(n)e-1)*n}_(n=1)^oo# converges to #1#.

We know that, #lim_(h to 0)(a^h-1)/h=lna, (a>0)#.

Now, to check whether the sequential limit for the seq. #{a_n}#

exists, we let, #h=1/n," so that, as "n to oo, h to 0#.

#:."The Seq. Lim.="lim_(n to oo)a_n#,

#=lim_(n to oo)(root(n)e-1)*n#,

#=lim_(n to oo){e^(1/n)-1}/(1/n)#,

#=lim_(h to 0)(e^h-1)/h#,

#=lne#.

#rArr"The Seq. Lim.="1#.

Consequently, the sequence #{(root(n)e-1)*n}_(n=1)^oo#

converges to #1#.