Sharky's experience on Metazhaghu

Sharky the famous astronaut was once sent into space (of course, in a spaceship), in search of a planet that is potentially habitable. However, due to some complication, Sharky accidentally lands on a planet called "Metazhaghu". This planet was a bit strange because the gravitational acceleration there was not constant. Sharky stood on a cliff and dropped a substance and found that the gravitational acceleration \(g\) becomes \(2g,3g,4g , \ldots\) for equal time intervals of \(t\).

Now Sharky from a certain height drops an object and that object hits the surface (ground) of Metazhaghu after such \(n\) time intervals. Find the height from ground of the place from where Sharky dropped the object.

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