Use mathematical induction to prove the following.0.04n < 0.04n-1

Question

What will be an ideal response?

Answer 1

Answers may vary. One possibility:
Sn: 0.04n < 0.04n-1
S1: 0.041 < 0.041-1
Sk: 0.04k < 0.04k-1
Sk+1: 0.04k+1 < 0.04k
Step 1: Since 0.041-1 = 0.040 = 1 and 0.041 < 1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
0.04k < 0.04k-1
0.04k0.04 < 0.04k-10.04 Multiplying by 0.04, 0.04 > 0
0.04k+1 < 0.04(k-1)+1
0.04k+1 < 0.04k.