This sequence of functions looks simple but

[unscientific]

Homework Statement

The question is attached in the picture.

The Attempt at a Solution

Since V₀ = 1,

Thus V₁ = $\stackrel{1}{2}$∏R² which is a constant.

Then shouldn't V_n be as in the picture?

 

[Sourabh N]

I think there is a typo in the question.

$(\sqrt{R^2 - x^2})$ should be $(\sqrt{R^2 - x^2})^n$

 

[unscientific]

I think there is a typo in the question.

$(\sqrt{R^2 - x^2})$ should be $(\sqrt{R^2 - x^2})^n$

hmm are u sure about that?

 

[Sourabh N]

Yes.

 

[Bacle2]

This seems to be the formula for the volume of an n-sphere:

http://en.wikipedia.org/wiki/N-sphere

 

[Ray Vickson]

Homework Statement

The question is attached in the picture.

The Attempt at a Solution

Since V₀ = 1,

Thus V₁ = $\stackrel{1}{2}$∏R² which is a constant.

Then shouldn't V_n be as in the picture?

$$V_1(R) = \int_{-R}^R V_0 \left(\sqrt{R^2-x^2} \right) \, dx = \int_{-R}^R \; 1 \, dx = 2R,$$
etc.

RGV