The value of
$$ 1 + \left(1 + \frac{1}{3}\right)\frac{1}{4} + \left(1 + \frac{1}{3} + \frac{1}{9}\right)\frac{1}{16} + \left(1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27}\right)\frac{1}{64} + \cdots $$
is:

Question

The value of  
$$ 1 + \left(1 + \frac{1}{3}\right)\frac{1}{4} + \left(1 + \frac{1}{3} + \frac{1}{9}\right)\frac{1}{16} + \left(1 + \frac{1}{3} + \frac{1}{9} + \frac{1}{27}\right)\frac{1}{64} + \cdots $$  
is:

Accepted Answer

![Screenshot 2025-04-02 192901.png](https://res.cloudinary.com/aptidude/image/upload/v1743602548/aptidude_questions/nub0bbe6se6gyywsptuw.png)

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