Consider the infinite sequence S₁ , S₂ , S₃ , S₄ , S₅ , S₆ , S₇ , S₈ , S₉ , … ,
which has S₁ = 1 and satisfies Sₙ = 2( Sn–1) + 1 for each integer n > 1.
[That is, for each integer n > 1, Sₙ equals 2 times the term with index n –1, plus 1.]
Prove (using mathematical induction): For each integer n ³ 1, Sn = 2ⁿ – 1 .
[That is, for each integer n ³ 1, Sₙ equals 2 raised to the n-th power, minus 1.]

Don’t forget to include both the basis step and the inductive step