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If L=lim(n rarr oo)((n)/(n^(2)+1^(2))+(...

If ` L=lim_(n rarr oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))+(n)/(n^(2)+3^(2))+....+(1)/(5n)) ` then the value of `tan L=`

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lim_(n rarr oo)((n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2)) + (n)/(n^(2)+3^(2))+......+(1)/(5n)) is equal to :

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

lim_(n rarr oo)(2^(3n))/(3^(2n))=

lim_(n rarr oo)(e^(2n)(n!)^(2))/(2n^(2n+1))

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

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

The value of lim_(n rarr oo)[(n)/(n^(2)+1^(2))+(n)/(n^(2)+2^(2))++(1)/(2n)] is

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

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