Use mathematical induction to prove the following.If a is a constant and 0 < a < 1, then an < 1.
What will be an ideal response?
Answers may vary. One possibility:
Sn: If a is a constant and 0 < a < 1, then an < 1.
S1: If a is a constant and 0 < a < 1, then a1 < 1.
Sk: If a is a constant and 0 < a < 1, then ak < 1.
Sk+1: If a is a constant and 0 < a < 1, then ak+1 < 1.
Step 1: Since it is given that a < 1, then a1 < 1. Therefore, S1 is true.
Step 2: Let k be any natural number. Assume Sk. Deduce Sk+1.
If a is a constant and 0 < a < 1, then ak < 1.
If a is a constant and 0 < a < 1, then ak ? a < 1 ? a. Multiplying by a, a > 0
If a is a constant and 0 < a < 1, then ak+1 < a.
If a is a constant and 0 < a < 1, then ak+1 < a < 1. Given a < 1
If a is a constant and 0 < a < 1, then ak+1 < 1.
You might also like to view...
Graph the equation.25y2 - 9x2 = 225
A. 
B. 
C. 
D. 
Subtract the fractions. Write the answer in lowest terms.
A. 
B. 
C. 
D. 
Simplify.320 - 34? 24 ÷ (4?3 - 2?2)
A. 474 B. 154 C. 717 D. 77
Write and solve an equation to answer the question. Round percent to the nearest thousandth, if necessary.The appliance store where the Scott family shops offers a 
for paying cash. The Scott family received a discount of $27. What was their total bill before the discount? Round to the nearest dollar.
A. $2 B. $200 C. $338 D. $3