heres the equation: http://img440.imageshack.us/img440/6467/untitledbw7.jpg
I showed that it was an alternate series, and i predicted that it converges absolutely, however i'm missing steps.
help is needed.
heres the equation: http://img440.imageshack.us/img440/6467/untitledbw7.jpg
I showed that it was an alternate series, and i predicted that it converges absolutely, however i'm missing steps.
help is needed.
Hello, rcmango!
Heres the series: .$\displaystyle \sum^{\infty}_{n=0}\frac{(-1)^nn}{\sqrt{1 + n^6}} $
I showed that it was an alternating series,
and i predicted that it converges absolutely.
However, i'm missing steps.
Comparison test
$\displaystyle \frac{n}{\sqrt{1 + n^6}} \:< \:\frac{n}{\sqrt{n^6}} \:=\:\frac{n}{n^3}\:=\:\frac{1}{n^2}$
Hence: .$\displaystyle \sum^{\infty}_{n=1}\frac{n}{\sqrt{1+n^6}} \:< \:\sum^{\infty}_{n=1}\frac{1}{n^2}$ . . . a convergent $\displaystyle p$-series
Therefore: .$\displaystyle \sum^{\infty}_{n=0}\frac{n}{\sqrt{1+n^6}}$ converges.