Which of the following represents a valid inductive step for proving , for all natural numbers n?

Question

Which of the following represents a valid inductive step for proving   , for all natural numbers n?

Answer

Assume 2 + 2 2  + 2 3  + . . . + 2 k  = k 2  , then prove the sum formula.

Answer

Assume the statement 2 + 2 2  + 2 3  + . . . + 2 k  = 2 k + 1  – 2, then show it holds for k + 1.

Answer

Assume the statement is true for k, then show it is true for n.

Answer

Assume the statement 2 + 2 2  + 2 3  + . . . + 2 k  = 2 k + 1  , then show it holds for k – 1.

Crowdly