1. What is the sum of the first n even positive integers? Prove your answer by induction.
2. Let α ∈ R and let n ∈ Z≥0 , and consider the arithmetic sequence hx0, x0 + α, x0 + 2α, . . .i. (Recall that each entry in an arithmetic sequence is a fixed amount more than the previous entry. Three examples are h1, 3, 5, 7, 9, . . .i, with x0 = 1 and α = 2; h25, 20, 15, 10, . . .i, with x0 = 25 and α = −5; and h5, 5, 5, 5, 5, . . .i, with x0 = 5 and α = 0.) An arithmetic sum or arithmetic series is the sum of an arithmetic sequence. For the arithmetic sequence hx0, x0 + α, x0 + 2α, . . .i, formulate and prove correct by induction a formula expressing the value of the arithmetic series
