Question

please how do I find the sum from k=1 to infinity of 3k/(k+4)

Answer 1

Divide everything by k

Answer 2

\[\sum_{k=1}^{\infty}\frac{3k}{k+4}\]Try to find a limit\[\lim_{k\rightarrow\infty}\frac{3k}{k+4}\]

Answer 3

are you looking for the sum??? the sum is unbounded as k goes to infinity...

Answer 4

3k/(k+4) =3(k+4-4)/(k+4)= 3(1-4/(k+4))
if k tends to infinity 4/k+4 tends to 0 hence the required sum is 3

Answer 5

the limit approaches to 3

Answer 6

so is this what you want? \(\large \sum_{k=1}^{\infty}\frac{3k}{k+4} \)

Answer 7

\[\lim_{k\rightarrow\infty}a_k\ne0\Rightarrow\sum_{k=1}^\infty a_k=\infty\]

Answer 8

Why are you guys changing the question? The asker said "sum from k=1 to infinity of 3k/(k+4)"

Isn't this what he want: \(\Large \sum_{k=1}^{\infty}\frac{3k}{k+4} \) ???
and not the limit?

Answer 9

finding the limit will enable us to determine whether it converges or diverges

Answer 10

\[\sum_{k=1}^{\infty}(\frac{ 3k }{ k+4 })=\infty\]

Answer 11

go for it then....

Answer 12

Like I said earlier, the sum is unbounded.....
http://www.wolframalpha.com/input/?i=sum+%283*k%29%2F%28k%2B4%29+from+k%3D1+to+infinity

Answer 13

Ooh, I screwed that up, sorry.....

Answer 14

as is stated above, the limit of the sequence (the summand) must converge to 0 or else the sum is undefined.
note: just because the limit of the summand goes to zero does *not* mean the series converges, just that it might.

Answer 15

limit as n->infty that is...

Answer 16

since the limit of the summand is not zero, we know the series does not converge, as was stated earlier

Answer 17

there are many other ways to see that this series does not converge btw

Answer 18

I'm getting confused

Answer 19

@Nastech just check the initial terms for k=1 , a1 = 3/4 , k=2, a2 =6/5 and for k=3 a3=9/7....if u see them clearly the series is always increasing and will reach to infinity for the infiniteth term...i.e summation of this series is unbounded or infinity

Answer 20

look, there are a number of tests for convergence
I think you should acquaint yourself with some
the one I think best for this series is the limit test

Answer 21

@Nastech do u get it now

Answer 22

the limit test is that for a sum\[\sum_{n=k}^\infty a_n\]if\lim_{n\to\infty}a_n\neq0\]then the series diverges, if \[\lim_{n\to\infty}a_n=0\]then it \(might\) converge, and we need another test to determine (ratio test, integral test, etc.)

Answer 23

edit*
if\[\lim_{n\to\infty}a_n\neq0\]then the series diverges, if

Answer 24

thanks a lot I get it now

Answer 25

are you posting a totally separate DE ?
please post each question separately, thanks.