If `lim _( x to oo) (r +2)/(2 ^(r+1) r (r+1))=1/k,` then k =

If lim _( n to oo) (r +2)/(2 ^(r+1) r (r+1))=1/k, then k =

Evaluate lim _( n to oo) sum_( r =1) ^(n -1) (1)/(sqrt(n ^(2) -r ^(2)))

lim_ (x rarr oo) sum_ (r = 0) ^ (n) ((1) / ((r + 2) n ^ (r)) =

If sum_(r = 1)^(oo) (1)/((2r - 1)^2) = (pi^2)/(8) then the value of sum_(r = 1)^(oo) (1)/(r^2) is

Let S _(K) = sum _(r=1) ^(k) tan ^(-1) (( 6 ^r)/( 2 ^( 2 r + 1) + 3 ^( 2r +1))) . Then lim _( k to oo) S _(k) is equal to :

The value of lim_(nto oo)(1)/(2) sum_(r-1)^(n) ((r)/(n+r)) is equal to

The value of lim_(nto oo)(1)/(2) sum_(r-1)^(n) ((r)/(n+r)) is equal to

lim_ (n rarr oo) sum_ (r = 2) ^ (n) ((r + 1) (sin pi) / (r + 1) -r (sin pi) / (r))