[Not Homework] Converging Series Problem (Fly and Einstein)

suporia
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This is not homework but a problem I would like to learn to solve before my exam.

Homework Statement



https://dl.dropbox.com/u/23889576/Screenshots/01.png

Homework Equations



Series Formulae

The Attempt at a Solution



I went about trying to determine a sum formula for the fly's distance traveled but could not get very far. Any help available would be appreciated. Thanks in advance.
 
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hi suporia! :wink:

show us how far you've got, and where you're stuck, and then we'll know how to help! :smile:
 
Hi,

I wasn't sure how to even start approaching the problem (determining the equation for the series).
 
suporia said:
I went about trying to determine a sum formula for the fly's distance traveled but could not get very far.

show us how far you did get :smile:
 
How long until they meet? If the fly is flying at 7 m/s how far does it fly in that time?
 

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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