There are two sequences:

$\displaystyle a_1,a_2,...; \:\:\:\:\:

b_1,b_2,...$ and each $\displaystyle a_i, b_i$ element of the sequences is 2 or 3. We know that:

$\displaystyle \frac 1 a_1 + \frac 1 {a_1a_2} + \frac 1 {a_1a_2a_3} + ... = \frac 1 b_1 + \frac 1 {b_1b_2} + \frac 1 {b_1b_2b_3} + ... $

Prove that the two sequences are equals.

Any help would be appreciated!