Arrey, the sum to infinity? It's a/(1-r) only. And this |r|<1 condition, it's like a fading memory, bhai – if it's smaller than one, it settles down nicely, otherwise it just runs away wildly. In my shop, I see this with old photo colours fading, like a geometric decay; the brightness decreases each year by a fixed ratio, so it never quite vanishes but finds a resting place. But honestly, that neat formula? Real life isn't so framed – a cherished memory's value doesn't decay, it grows, so sometimes r feels greater than one in the heart.
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