Proving Limit Exists with Cauchy Criterion for {X_n}

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Your N is not fixed; it should depend on \varepsilon only.

What's s?
Why did you pick p = 1?
 
mutton said:
Your N is not fixed; it should depend on \varepsilon only.

What's s?
Why did you pick p = 1?

give me a reason y i can't pick p=1

and bout the Sn
Sn= sum of the series from a1 to an

.
 
No one has to give you a reason why you can't pick p= 1. You are the one who is doing this. Please answer the question- why DID you pick p= 1?
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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