" 13.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 "

Let u_(n)=sum_(k=1)^(n)(k) and v_(n)=sum_(k=1)^(n)(k-0.5) . Then lim_(n rarr oo)(sqrt(u_(n))-sqrt(v_(n))) equals

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

For n in N, let a_(n)=sum_(k=1)^(n)2k and b_(n)=sum_(k=1)^(n)(2k-1)* then lim_(n rarr oo)(sqrt(a)_(n)-sqrt(b_(n))) is equal to

lim_(n rarr oo)(n!)/((n+1)!+n!) is equal to

lim_(n rarr oo)(n!)/((n+1)!+n!) is equal to

Consider the sequence u_(n)=sum_(r=1)^(n)(r)/(2^(r)),n>=1 then the lim it_(n rarr oo)u_(n)

Let a sequence whose n^(th) term is {a_(n)} be defined as a_(1)=(1)/(2) and (n-1)a_(n-1)=(n+1)a_(n) for n>=2 then lim_(n rarr oo)S_(n), equals

Let S_(n)=(n)/((n+1)(n+2))+(n)/((n+2)(n+4))+(n)/((n+3)(n+6))+............+(1)/(6n) then lim_(n rarr oo)S_(n) has the value equal to

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