Why {x^n} /\sum_{0}^{x}x^{n-1}={x-1}/x: Explained

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The equation {x^n} /\sum_{0}^{x}x^{n-1}={x-1}/x raises questions regarding the absence of "n" in the summation. Concerns are highlighted about the left side being non-zero at x=1, while the right side equals zero at the same point, indicating a potential inconsistency. The discussion suggests that further clarification or explanation from the original source is needed to resolve these discrepancies. Participants express skepticism about the validity of the exercise as it stands. Overall, the equation's formulation appears problematic and requires additional scrutiny.
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Can anyone proove why {x^n} /\sum_{0}^{x}x^{n-1}={x-1}/x
 
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Rewrite done.
 
It doesn't look sound to me.If you sum over "x",why doesn't "n" appear in the equation...?

Daniel.
 
Also, in its current form, the Right Side is 0 at x=(1), whereas the Left Side is non-zero at x=(1).
 
There's definitely something weird with this exercise.Maybe he'll explain it,or or just drop it...

Daniel.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
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