Does the Series 1.05^n/n^5 Converge or Diverge?

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Homework Statement



Summation from 1 to infinity of 1.05^n/n^5

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The Attempt at a Solution


Lost. I'm not sure if the ratio test would apply here.. convergence tests are definitely not my strong point!
 
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Does the limit of \frac{1,05^n}{n^5} approach 0? What can you conclude from this?
 
No, it would approach infinity, right? Meaning that it diverges?
 
Yes, so you can conclude that the series diverges.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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