Question

series and sequences:

Answer 1

\[a_{n}=\frac{ 2n }{ 3n+1 }\] does the sequence converge or diverge? can someone help me with this one?

Answer 2

converge to 2/3

Answer 3

Because the +1 is not relevant at infinity. 2n/3n
plug in "infinity or a large number" and it will be approaching 2/3

Answer 4

I got the same, now what about \[\sum_{n=1}^{\infty}a_{n}\] ? shouldn't it converge as well?

Answer 5

That would be a fibonacci sequence,

Answer 6

if you google it you will see, They are a bit more complicated, because a to the subsccript n just signifies the nth term is the sum.

Answer 7

And honestly, i do not know the answer to that fibonacci sequence.

Answer 8

is the sum of the sequence, I thought that finding whether the sequence was convergent or not I could determine the same for the series