Use mathematical induction to prove the following.3n > n
What will be an ideal response?
Answers may vary. One possibility:
Sn: 3n > n
S1: 31 > 1
Sk: 3k > k
Sk+1: 3k+1 > k + 1
1. Basis step: Since 31 > 1, S1 is true.
2. Induction step: Let k be any natural number. Assume Sk. Deduce Sk+1.
3k > k
3k ? 3 > k ? 3 Multiplying by 3, 3 > 0
3k+1 > k(1 + 2)
3k+1 > k + 2k
2k ? 1 2 ? 1 and k ? 1
3k+1 > k + 1
You might also like to view...
Provide an appropriate response.Solve the inequality: 
> 0
A. -1 < x < 3 B. x < -1 or x > 3 C. x < -3 or x > 1 D. -3 < x < 1
Find all solutions to the equation. Express the solution in degrees.sin x = - 
A. 45° + 360°n or 315° + 360°n B. 225° + 360°n or 315° + 360°n C. 135° + 360°n or 315° + 360°n D. 240° + 360°n or 300° + 360°n
Complete the table of values for the given equation.5x - 5y = -25
A. 0; 5; -5 B. 10; 5; -5 C. 10; -5; 5 D. 0; -5; 5
Solve.A rectangular field has a perimeter of 372 yd. The width of the field is 48 yd less than the length. What are the dimensions of the field?
A. Length: 117 yd, width: 81 yd B. Length: 234 yd, width: 69 yd C. Length: 101 yd, width: 85 yd D. Length: 117 yd, width: 69 yd