Series Convergence: Can I Create a p-Series?

Dissonance in E
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Homework Statement



infinity
SIGMA sqrt(n) / ((n^2)(ln(n))
n = 2

Homework Equations





The Attempt at a Solution



Could i beat this into a p-series perhaps?
 
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Dissonance in E said:

Homework Statement



infinity
SIGMA sqrt(n) / ((n^2)(ln(n))
n = 2

Homework Equations





The Attempt at a Solution



Could i beat this into a p-series perhaps?
You can't "beat" it into a p-series, but you can compare it to a convergent p-series.
 
Ah I see, thank you.
 
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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