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

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)

Q.if f(n,theta)=prod_(r=1)^(n)(1-tan^(2)((theta)/(2^(t)))), then compute lim_(n rarr oo)f(n,theta)

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

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)

Let P=(prod_(r=1)^(45)sin(r^(@)))(prod_(k=46)^(89)sec(k^(@))) then (i)sin^(-1)P=(pi)/(6)( ii) cot^(-1)(log_(2)P)=pi-tan^(-1)(2)( iii) cot^(-1)(sqrt(2^(log_(P)(2))))=cot^(-1)((1)/(P^(2)))( iv )sin^(-1)(sin P)=pi-P

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

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

If for n ge 1, P_(n) = int_(1)^( e) (log x)^(n) dx , then P_(10) - 90P_(8) is equal to