`lim_(n->oo)prod_(r=3)^n(r^3-8)/(r^3+8)`

Number of solutions of the equation csctheta=k in [0,pi] where k=lim_(n->oo)prod_(r=2)^n((r^3-1)/(r^3+1)) is ____

Number of solutions of the equation cosectheta=k in [0,pi] where k=lim_(n->oo)pi_(r=2)^n((r^3-1)/(r^3+1)) is

Let lambda=int_0^1(dx)/(1+x^3),p=(lim)_(n->oo)[(prod_(r=1)^n(n^3+r^3))/(n^(3n))]^(-1/n) then ln p is equal to (a) ln2-1+lambda (b) ln2-3+3lambda (c) 2ln2-lambda (d) ln4-3+3lambda

Let lambda=int_0^1(dx)/(1+x^3), p=lim_(n rarr oo)[prod_(r=1)^n(n^3+r^3)/(n^(3n))]^(1//n) then ln p is equal to (a) ln2-1+lambda (b) ln2-3+3lambda (c) 2ln2-lambda (d) ln4-3+3lambda

Show that Lim_(ntooo)prod_(r=1)^(n)r/(r^(4)+r^(2)+1)=1/2

Number of solutions of the equation cos ec theta=k in[0,pi] where k=lim_(n rarr oo)pi_(r=2)^(n)((r^(3)-1)/(r^(3)+1)) is

The value of lim_(n rarr oo)prod_(r=0)^(n)(1+(1)/(2^(2^(r)))) is

The value of lim_(n to oo) sum_(r=1)^(n)(r^(2))/(r^(3)+n^(3)) is -

The value of lim_(n to oo) sum_(r=1)^(n)(r^(2))/(r^(3)+n^(3)) is -

lim_(n to oo) sum_(r=1)^(n) ((r^(3))/(r^(4) + n^(4))) equals to-