/sci/ - Science & Math

>>11610414
>throw the polynomial in wolfram alpha
>absolutely immense
Eh, even if we can't factor, we can always compare.

We take [math]a=1[/math] and [math]b=3[/math].
Then [eqn]n \times \frac{n^2+n+1}{n^3+n+1} = \frac{n^3+n^2+n}{n^3+n+1}[/eqn]
Now, [math]n^3=n^3[/math], [math]n^2 \geq n[/math] (for [math]n \geq 1[/math] ) and [math]n \geq 1[/math] (again for [math]n \geq 1[/math] , tautologically). Thus [eqn]\frac{n^3+n^2+n}{n^3+n+1} \geq 1[/eqn] and consequently [eqn]\frac{n^2+n+1}{n^3+n+1} \geq \frac{1}{n}[/eqn].
Now, since this comparison tells us that [eqn] \sum_{i=1}^{\infty} \frac{n^2+n+1}{n^3+n+1} [/eqn]diverges and we know that [eqn]\sum_{i=1}^{\infty} \frac{n+3}{n^3+n+1}[/eqn] converges, the original series also diverges.

>>11134861
This really looks like the kind of problem where you just swap sin and cos for the power expansions, use the ole rule for integration of power series, and evaluate by hand like a retard, did you try doing that?
>>11134743
Seems like the book is wrong to me.