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

Show that the square root of 3^((1)/(2))xx9^((1)/(4))xx27^((1)/(8))xx81^((1)/(16))xx... to infinity is 3. [ Note : When we are asked to find the square root of a number, it is presumed that we have to find the principal square root.] Find the sum of the series (1)/(2)+(2)/(4)+(3)/(8)+(4)/(10)+...oo and substitute in (1).]

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

Find 1-(1)/(2)+(1)/(4)-(1)/(8)+(1)/(16)-(1)/(32)+......oo

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

2.4^((-1)/(4))*8^((1)/(9))*16^((-1)/(16))*32^((1)/(25))*64^((-1)/(36))*……….oo=

Evaluate ((1)/(4))^(-2)-3(8)^(2//3)xx4^(0)+((9)/(10))^(-1//2)

Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)oo=6.

Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)oo=6.

Prove that: 3^(1/2)xx3^(1/4)xx3^(1/8)xx...=3

Evaluate : [(1)/(4)]^(-2)-3(8)^((2)/(3)) xx 4^(0) + [(9)/(16)]^(-(1)/(2))