Let `P=prod_(n=1)^oo(1 0^(1/(2^(n-1))))` then find `log_0.01 P`.

Let P=prod_(n=1)^(oo)(10^((1)/(2n-1))) then find log_(0.01)P

Let L=prod_(n=3)^(oo)(1-(4)/(n^(2)));M=prod_(n=2)^(oo)((n^(3)-1)/(n^(3)+1)) and N=prod_(n=1)^(oo)((1+n^(-1))^(2))/(1+2n^(-1)), then find then find the value of L^(-1)+M^(-1)+N^(-1)

Let P_(n)=prod_(k=2)^(n)(1-(1)/((k+1)C_(2))). If lim_(n rarr oo)P_(n) can be expressed as lowest rational in the form (a)/(b), find the value of (a+b)

The value of the limit prod_(n=2)^(oo)(1-(1)/(n^(2))) is

Let lambda=int_(0)^(1)(dx)/(1+x^(3)),p=(lim)_(n rarr oo)[(prod_(r=1)^(n)(n^(3)+r^(3)))/(n^(3n))]^(-) then ln p is equal to (a)ln2-1+lambda(b)ln2-3+3 lambda(c)2ln2-lambda(d)ln4-3+3 lambda

p=sum_(n=0)^(oo) (x^(3n))/((3n)!) , q=sum_(n=1)^(oo) (x^(3n-2))/((3n-2)!), r = sum_(n=1)^(oo) (x^(3n-1))/((3n-1)!) then p + q + r =

Find the value of prod_(n-2)^(n) (1 - (1)/(n^(2)))

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