Question

Using Newton's binomial formula. Find the sum of...

Answer 1

Using Newton's binomial formula. Find the sum of...

\[\sum_{k=0}^{n} \left(\begin{matrix}n \\k\end{matrix}\right)\]

Answer 2

this represents one row of pascal's triangle, so the sum is \(2^n\)
not sure what "newtons binomial formula" is but i guess you can prove it by induction

Answer 3

actually if you want a snap proof, compute \(2^n\) as \((1+1)^n\) and you will have your result instantly

Answer 4

how do you know it's the first row of pascal's triangle?

Answer 5

it is not the first row, it is the nth row

Answer 6

i said "one row" which was not precise
in any case if you use the binomial formula for \((1+1)^n\) you get your result

Answer 7

i get it. but how did you come to \[2^{n}\]
?