Learn to use induction to prove that the sum formula works for every term

What is the first step in proving a sum formula by induction?

• Disprove the formula for the first term

• Assume the formula is true for all terms

• Verify the formula for the first term

• Prove the formula for the last term

In the induction hypothesis, what is the expression for the sum up to K terms?

• K^3 + 1

• K^2 * (K + 1)^2 / 4

• K^3 / 4

• K^2 + K + 1

What is the goal of the induction step in this proof?

• To prove the formula for K + 2

• To verify the formula for the first term

• To prove the formula for K + 1

• To disprove the formula for K

Which common term is factored out during the algebraic manipulation?

• K^3

• K + 2

• K + 1

• K^2

What is the simplified form of the trinomial K^2 + 4K + 4?

• (K + 2)^2

• (K + 1)^2

• K^2 + 4K + 2

• K^2 + 2K + 1

What is the purpose of multiplying by 4/4 during the proof?

• To convert the expression to a fraction

• To factor out a common term

• To change the base of the expression

• To simplify the expression

What does the conclusion of the induction proof confirm?

• The formula is valid for all natural numbers

• The formula is valid for some natural numbers

• The formula is invalid for all natural numbers

• The formula is valid only for even numbers