The value of `flim_(n->oo){(sqrt(2)+1)^n}(-1)^[[(sqrt(2)+1)^(n)], n in Z` is (where[.] denotes G I F and {.} denotes fractional part function)

lim_(n->oo) ((sqrt(n^2+n)-1)/n)^(2sqrt(n^2+n)-1)

The value of lim_(n rarr oo)[3sqrt((n+1)^(2))-3sqrt((n-1)^(2))] is

The value of lim_(n->oo)(sqrt(1)+sqrt(2)+sqrt(3)+.....+sqrt(n))/(nsqrt(n)) is

lim_(n->oo){sqrt(3)+1}^n+(-1)^(sqrt(3)+1)^7] ={L when n is even and M,when n is odd ({.} & [.] denote fractional part and greatest integer function respectively) then L + M =

The value of lim_(nto oo)(sqrt(n^(2)+n+1)-[sqrt(n^(2)+n+1)]) where [.] denotes the greatest integer function is

The value of lim_(nto oo)(sqrt(n^(2)+n+1)-[sqrt(n^(2)+n+1)]) where [.] denotes the greatest integer function is

lim_(n rarr oo){(sqrt(5)+2)^(n)}*cos(pi[(sqrt(5)+2)^(n)] is equal to (where n in I and [], {.} denotes greatest integer function and fractional part function respectively)

If l=int_(0)^(1//2)(dx)/(sqrt(1-x^(2n))), n in N then (Where, [.] denotes G.I.F)

If l=int_(0)^(1//2)(dx)/(sqrt(1-x^(2n))), n in N then (Where, [.] denotes G.I.F)