I dont know whats wrong with me...I have been studing for 6 hrs straight...and i noticed I have been making stupid mistakes...so can somone tell me whats up with my work...this is what I did. [tex]\sum_{n=2}^{\infty}\frac{1}{nln(n)}[/tex] must show if it converges or diverges soooo this is what i did(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int_{2}^{\infty}\frac{1}{nln(n)}dn[/tex] integration by parts and

[tex] u=\frac{1}{ln(n)}[/tex] ,

[tex]du=\frac{1}{n(ln(n))^2}[/tex] ,

[tex]v=ln(n)[/tex] ,

[tex]dv=\frac{1}{x}[/tex]

[tex]\int_{2}^{\infty}\frac{1}{nln(n)}dn[/tex]=[tex]\frac{ln(n)}{ln(n)}-\int_{2}^{+\infty}\frac{ln(n)}{nln(n)^2}dn[/tex]

my logarithms cancel out and become [tex]1[/tex] and my integral of logorithms the top cancels and becomes one and i add it to the other side divide by two and i get [tex]\frac{1}{2}[/tex] now which say it converges did I do that right?

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