At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
you can simply take values or take the limit as x --> infinity^_^
the limit as x-->infinite is zero, which is inconclusive
no no, it means that the series converge ^_^
when you end up with zero, it means the series is converging :) and when you end up with infinity it diverges
the series will not necessarily converge when the limit of the sequence as n-->infinite is zero, for example 1/n
Sorry sstarica, that is not correct
I need another test
prifk is right
i was thinking limit comparison or ratio
but ratio yields "1", inconclusive.. and not sure what converging or diverging series to limit compare to
Simplifying a bit will help here..\[(n*2^n)/(2^n + 3^n) = n/[1 + (3/2)^n]\]
yes, I did that. not sure what the next steps are ... l'hopitals rule says the limit goes to zero
perhaps a comparison of some sort?
this question was driving me mad and I'm a tutor lol!
You tried the ratio test?
i'll try again
yeah, still 1
converge. Ask hinted by polpak, write (n*2^n)/(2^n + 3^n) as n/[1 + (3/2)^n]. Then compare this with n(2/3)^n which is convergent by the Ratio test
well done! thank you