Binomial Theorem. For any n E {0,1,2, ..} and any a and b, (a + b)" = E-o G)albn-i. %3D %3D0 Exercise 3. (a) Argue that E"-o G) = 2" and verify this result by summing for each n e {2,3,4}. %3D j%30...

Only e part


Extracted text: Binomial Theorem. For any n E {0,1,2, ..} and any a and b, (a + b)" = E-o G)albn-i. %3D %3D0 Exercise 3. (a) Argue that E"-o G) = 2" and verify this result by summing for each n e {2,3,4}. %3D j%30 (b) Argue that E-o(-1) (G) = 0 and verify this result by summing for n = 4. %3D (c) Evaluate 53 = (2 + 3) directly and also as a sum of 4 terms using the Binomial Theorem. (d) Evaluate 1.8* = (2 - 0.2)* directly and also as a sum of 5 terms using the Binomial Theorem. (e) Argue that E-0 () p'(1- p)"- = 1, for any 0s ps1. (Use 0° = 1.)