If `3+1/4(3+p)+1/(4^2)(3+2p)+... + oo=8`, then p

Let p= 3^(1//3) .3^(2//9).3^(3//27) ….oo then p^(1//3) =

P=3^((1)/(3))3^((2)/(9))3^((3)/(27))...oo, then P^((1)/(3)) is

4p−(3p−1​)=1−(2p−2​)

If |{:(2, -3), (p-4, 2p-1):}| = -6 , then p =____.

Let P_ (n) = (2 ^ (3) -1) / (2 ^ (3) +1) * (3 ^ (3) -1) / (3 ^ (3) +1) * (4 ^ ( 3) -1) / (4 ^ (3) +1) ...... (n ^ (3) -1) / (n ^ (3) +1) Prove that lim_ (n rarr oo) P_ ( n) = (2) / (3)

If (1+4p)/(4),(1-p)/(3) and (1-2p)/(2) are the probabilities of three mutually exclusive events then values of p may be