Follow the outline below and use mathematical induction to prove the Binomial Theorem:

a. Verify the formula for n = 1.

b. Replace n with k and write the statement that is assumed true. Replace n with k + 1 and write the statement that must be proved.

c. Multiply both sides of the statement assumed to be true by a + b. Add exponents on the left. On the right, distribute a and b, respectively.

d. Collect like terms on the right. At this point, you should have

e.

f.

Transcribed Image Text:

n n (a + by² = (")a" + (")a^¹−¹b + (2) α¹-²6² b)n an- 1-262 + + n ( ₁²₁1 ) abr-1 ·(n)b¹. +