So either your book is wrong or else you are misreading it.
for positive , and so2)
book says convergent but i think divergent
this time i think an>(1+n)/(n+n^2)=1/n
Again, either your book is wrong or else you're misreading it.
It is not true that .3) an=1/[n ln(n)] convergent
compare with un=1/n^2 so an/un=n/ln(n) which tends to 1
Instead, use the integral test. Letting , we have
Notice that for positive . So4) an=ln(n)/n^2..
i think convergent but not sure how to show this.
This does indeed follow from (4).5) an=ln (n)/(2n^3-1)
as for 4. think convergent but not doing correct comparison.
Use inequalities instead of trying to multiply out. For example,5) an=(2n-1)/n(n+1)(n+2)
this converges, i put into partial fractions and got an expression for the sum. Is there a nice comparison to show it quicker?
And of course the comparison test will work quite easily here.