Proving a theorem about limits

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a) Suppose that the limit as n goes to infinity sn=0. If (tn) is a bounded sequence, prove that lim(sntn)=0.
So I need to show that abs(sntn)<epsilon, and I know that abs(sn)<epsilon. I mean, I know abs(sntn)=abs(sn)abs(tn that didn't help.
I don't know how to go about this. I've tried the triangle inequality variations but that didn't seem to get me anywhere either. I feel like I'm going in circles.
can I get a hint?

thanks!
 
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say M is a bound of the sequnce t_n, can you show M.s_n tends to zero?
 
thanks, I finally figured it out!
mjjoga
 

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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