The product `2^((1)/(2)) . 4^(1/(8)) . 8^((1)/(16) …"to" oo` equal to

Show that 9^(1/(4)).9^(1/(8)).9^(1/(16).) . .."to" oo = 3

The value of 2^(1/4).4^(1/8).8^(1/16),,,,,,,oo is equal to.

Show that X^((1)/(2))*X^((1)/(4))*X^((1)/(8)) ... Upto oo = X

lim_(x to 1//2) (8x^(3) - 1)/(16 x^(4) - 1) is equal to

Show that 2^((1)/(4))xx4^((1)/(8))xx8^((1)/(16))xx16^((1)/(32))xx.... oo=2.

The sum of the series cot^(-1)((9)/(2))+cot^(-1)((33)/(4))+cot^(-1)((129)/(8))+…….oo is equal to :

Prove that: a^(1/2).a^(1/4).a^(1/8),…….to oo=a.

The sum (2^(1))/(4^(1) - 1) + (2^(2))/(4^(2) - 1) + (2^(4))/(4^(4) - 1) + (2^(8))/(4^(8) - 1) +... oo is equal to (A) 2 (B) 1 (C) 3 (D) 5

Prove that: 2^(1/4).4^(1/8), 8^(1/16). 16^(1/32)......... oo=2 .

Value of (1+1/3)(1+1/(3^2))(1+1/(3^4))(1+1/(3^8))........oo is equal to a. 3 b. 6/5 c. 3/2 d. none of these