Chapter 8, Sequences and Series - Section 8.6 - The Binomial Theorem - 8.6 Exercises - Page 637: 58

See explanation

Adding the first row gives us 2, the second gives us 4, the third gives us 8, and then 16 and then 32. Epiphany! These are the powers of 2. Thus, the pattern is the $nth$ row sums to $2^n$. Expanding $(1+1)^n$ gives us $1+C(n,1) + C(n,2) +... C(n,n)=2^n$ which matches what we have.