The purpose of the following questions is to develop Wallis's formula which has many applications. In particular,
for the proof of the Stirling's Formula. For *n*=0,1,2.., define

**1**- Show that , for every n.
**2**- Show that for all , we have
**3**- Prove that
**4**- Prove that
**5**- Conclude that
**6**- Prove that

Note also that the above product can be expressed using factorials. Try to come up with the formula translating the above limit using factorials.

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