Sum of Entries in Row of Pascal's Triangle/Proof 1

Theorem

The sum of all the entries in the $n$th row of Pascal's triangle is equal to $2^n$.

Proof

By definition, the entries in $n$th row of Pascal's triangle are exactly the binomial coefficients:

$\dbinom n 0, \dbinom n 1, \ldots, \dbinom n n$

The result follows from Sum of Binomial Coefficients over Lower Index.

$\blacksquare$

Sources

• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $35$