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

Question

anonymous · Answer

Using Newton's binomial formula. Find the sum of...

$$\sum_{k=0}^{n} \left(\begin{matrix}n \k\end{matrix}\right)$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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