(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Study the convergence of the following sequences

a[itex]_{n}[/itex] = [itex]\int^{1}_{0}[/itex] [itex]\frac{x^{n}}{1+x^{2}}[/itex]

b[itex]_{n}[/itex] = [itex]\int^{B}_{A}[/itex] sin(nx)f(x) dx

3. The attempt at a solution

For the first one, I said it was convergent. I'm not exactly sure why though, my reasoning was something like this

for all values n>0, the sequence is increasing. It seems to be bounded by 1/2? (not sure here, the integral is messing me up)an increasing sequence that is bounded is also convergent.

The second one, I'm not even sure where to start. Maybe an integration by parts which would end up to repeat itself, as that's what I think I see.

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# Homework Help: Investigating the convergence of a sequence

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