<s>[INST] Express the following product as a single fraction: $(1+\frac{1}{3})(1+\frac{1}{9})(1+\frac{1}{81})\cdots$ 
I'm having difficulty with this problem:
What i did was:
I rewrote the $1$ as $\frac{3}{3}$
here is what i rewrote the whole product as:
$$\left(\frac{3}{3}+\frac{1}{3}\right)\left(\frac{3}{3}+\frac{1}{3^2}\right)\left(\frac{3}{3}+\frac{1}{3^4}\right)\cdots\left(\frac{3}{3}+\frac{1}{3^{2^n}}\right)$$
but how would i proceed after this?
 [/INST] Recall the difference of squares formula $$a^2 - b^2 = (a+b)(a-b).$$  With the special case $a = 1$, $b = x^n$, we would get $$1 - x^{2n} = (1-x^n)(1+x^n).$$  What does this suggest?
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