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

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.

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.

Does

_{\large{_{4}C_{0} + _{4}C_{1} + _{4}C_{2} + _{4}C_{3} + _{4}C_{4} = 2^{4}}}?See part (a).

Explain why

._{\large{_{n}C_{0} + _{n}C_{1} + _{n}C_{2} + …+ _{n}C_{n} = 2^{n}}}Any reasonable explanation is acceptable.