### Home > A2C > Chapter 12 > Lesson 12.4.2 > Problem12-187

12-187.

Duong noticed that $\large{_{1}C_{0} + _{1}C_{1} = 2^{1}}$. He tried $\large{_{2}C_{0} + _{2}C_{1} + _{2}C_{2} = 2^{2}}$ and found that it worked also.

1. Does $\large{_{3}C_{0} + _{3}C_{1} + _{3}C_{2} + _{3}C_{3} = 2^{3}}$?

Use your calculator to test the expression.

Yes, it also works.

2. Does $\large{_{4}C_{0} + _{4}C_{1} + _{4}C_{2} + _{4}C_{3} + _{4}C_{4} = 2^{4}}$?

See part (a).

3. Explain why $\large{_{n}C_{0} + _{n}C_{1} + _{n}C_{2} + …+ _{n}C_{n} = 2^{n}}$ .

Any reasonable explanation is acceptable.