Question

How did they simplify this matrix?

Answer 1

It started out like this \[\sum_{n=k}^{\infty}\left(\begin{matrix}n \\ k\end{matrix}\right)(\frac{ z }{ n })^n\]

Answer 2

and it became this \[\lim_{n \rightarrow \infty} \left| \frac{ \left(\begin{matrix}n \\ k\end{matrix} \right) \times \frac{ 1 }{ 2n^n }}{ \left(\begin{matrix}n+1 \\ k\end{matrix}\right) \times \frac{ 1 }{ 2^{n+1} }} \right|\]

Answer 3

\[\lim_{n \rightarrow \infty} \left| \frac{ 2(n-k+1) }{ n+1 } \right| =2\]

Answer 4

This is complex vector analysis I understand the theory but I just don't get how they simplify all this n k stuff

Answer 5

try substitution

like n=0,n=1,n=k ....
i guess ..

Answer 6

well I just want to know how they got from the second equation I posted to knowing that it's 2(n-k+1) / n+1

Answer 7

i think simplifying ...

@karatechopper

Answer 8

Yeah I forgot how to simplify binomial series..

Answer 9

sorry..I don't know how to solve this..

Answer 10

Do you know how to simplify (n k) / (n +1 k)

Answer 11

to get (n-k+1)/(n+1)?