9. Sequences, Series, & Induction

In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n. n + 2 > n

In Exercises 25–34, use mathematical induction to prove that each statement is true for every positive integer n. n Σ (i = 1) 5 · 6ⁱ = 6(6ⁿ - 1)

Use mathematical induction to prove that the statement is true for every positive integer n. 1 + 4 + 4^2 + ... + 4^(n-1) = ((4^n)-1)/3

Use mathematical induction to prove that the statement is true for every positive integer n. 5 + 10 + 15 + ... + 5n = (5n(n+1))/2

In Exercises 5–10, a statement Sn about the positive integers is given. Write statements S_k and S_k+1 simplifying statement S_k+1 completely. Sn: 3 + 7 + 11 + ... + (4n - 1) = n(2n + 1)