Question

Use the principle of mathematical induction to prove that:
1 - 2² - 2³ ⋅ (-1)ⁿ 2ⁿ = (2(n - 1) ⋅ (-1)ⁿ) / 3 for all positive integers n.

a) Base case: n = 1
b) Base case: n = 2
c) Base case: n = 3
d) Base case: n = 4