For n ≥ 1, derive each of the identities below:(a) .[Hint: Let a = b = 1 in the binomial t...

For n ≥ 1, derive each of the identities below:

(a) .

[Hint: Let a = b = 1 in the binomial theorem.]

(b) .

(c) .

[Hint: After expanding n(1 + b)n−1 by the binomial theorem, let b = 1; note also that

(d) .

(e) .

[Hint: Use parts (a) and (b).]

(f) .

[Hint: The left-hand side equals