Question

Prove that : (3^1/2)×(3^1/4)×(3^1/8)×………..=3​​

Answer 1

Answer:

3^(1/2 + 1/4 + 1/8 + ... ) = 3^1 = 3

Step-by-step explanation:

3^1/2 * 3^1/4 * 3^1/8 ... = 3

3^(1/2 + 1/4 + 1/8 + ... ) = 3

Now we look at 1/2 + 1/4 + 1/8 + ...

1/2 + 1/4 + 1/8 + 1/16 + · · · is an elementary example of a geometric series

The sum of this series can be denoted in summation notation as:  1/2 + 1/4 + 1/8 + 1/16 + · · · = (1/2) / ( 1 - 1/2 ) = 1

-From here it is obvious that 3^(1/2 + 1/4 + 1/8 + ... ) = 3^1 = 3