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

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

For n in N, prove that (n+1)[n!n+(n-1)!(2n-1)+(n-2)!(n-1)]=(n+2)!

If f(n)=(1)/(n){(n+1)(n+2)(n+3)...(n+n)}^(1//n) then lim_(n to oo)f(n) equals

If A={x : x=n , n in N} , B={x : =2n , n in N} , c={x : x =4n , n in N} , then

If f(n)=(-1)^(n-1)(n-1),G(n)=n-f(n) for every n in N then (GOG)(n)=

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

Prove that : (i) (n!)/(r!)=n(n-1)(n-2)...(r+1) (ii) (n-r+1)*(n!)/((n-r+1)!)=(n!)/((n-r)!) (iii) (n!)/(r!(n-r)!)+(n!)/((r-1)!(n-r+1)!)=((n+1)!)/(r!(n-r+1)!)

Let U_(n)=(n!)/((n+2)!) where n in N. If S_(n)=sum_(n=1)^(n)U_(n), then lim_(n rarr oo)S_(n), equals