1.

Prove that: `2^(1/4).4^(1/8), 8^(1/16). 16^(1/32)......... oo=2`.A. 1B. 2C. `3//2`D. `5//2`

Answer» Correct Answer - B
We have,
`2^(1//4)*4^(1//8)*8^(1//16)*16^(1//32) . . .. . .oo`
`=2^(1//4+2//8+3//16+4//32_. .. . . . . . .oo`

`=2^(2^(1/2+)2^(2/3+)2^(3/4+)2^(4/5+) . . . . . . . .`
`=2^(2^(1/2){1+(2)/(2)+(3)/(2^(2))+(4)/(2^(3))}`
`2^(2^(1/2){(1)/(1-(1)/(2))+(1xx1//2)/(1-(1)/(2))^(2)}_(=2+(1)/(4)(2+2)_(=2^(1)=2)))`


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