- #1

utkarshakash

Gold Member

- 855

- 13

## Homework Statement

{a_n} and {b_n} are two sequences given by [itex]a_n = (x)^{1/2^n}+(y)^{1/2^n} [/itex] and

[itex]b_n = (x)^{1/2^n}-(y)^{1/2^n}[/itex]. Then find [itex]a_1 a_2 a_3 ..... a_n [/itex] in terms of x,y and b_n

## Homework Equations

## The Attempt at a Solution

I tried substituting n=1,2,3 and so on for a few terms of a_n but really couldn't see anything important. I tried finding x and y instead in terms of a_n and b_n and got this

[itex]x =\left( \dfrac{a_n + b_n}{2} \right) ^{2^n} \\

y = \left( \dfrac{a_n - b_n}{2} \right) ^{2^n}[/itex]