Question

solve this question please​

Answer 1

SEE THE AATACHMENT YOUR ANSWER IS THIS AND I THINK IT IS CORRECT

#TOGETHER WE GO FAR✔✔

Answer 2

Answer:

Try writing every term in your product as a power of 3. So,

3^(1/3) = 3^(1/3)

9^(1/9) = 3^(2/9)

27^(1/27) = 3^(3/27),

and so forth. Then, your infinite product becomes

3^(1/3) * 3^(2/9) * 3^(3/27) * ...,

which can now be written as

3^[1/3 + 2/9 + 3/27 + ... ]

where the exponent is an infinite sum. Now the task becomes how to

evaluate this infinite sum. This can be done by writing it as an

infinite sum of infinite sums, like this

1/3 + 1/9 + 1/27 + 1/81 + ... = 1/2

1/9 + 1/27 + 1/81 + ... = 1/6

1/27 + 1/81 + ... = 1/18

1/81 + ... = 1/54

... = ...

_________________________________________

1/3 + 2/9 + 3/27 + 4/81 + ... = (1/2)[1 + (1/3) + (1/9) + ... ]

= 3/4.

★ So it looks like the answer to your

infinite product is 3^(3/4).