Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.1 + 3 + 32 + ... + 3n - 1 = 
What will be an ideal response?
First, we show that the statement is true when n = 1.
For n = 1, we get 1 (or 3[(1) - 1]) = 
= 
= 1.
This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,
is true for some positive integer k.
We need to show that the statement holds for 
. That is, we need to show that
So we assume that 
is true and add the next term, 3k, to both sides of the equation.
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
You might also like to view...
Find the book value using the MACRS method of depreciation and the MACRS depreciation rates table. Round to the nearest dollar.MACRS Depreciation Rates 
Cost: $167,000Recovery Period: 7-yearAfter: Fourth year
A. $20,858 B. $76,954 C. $52,171 D. $48,096
Solve.2x2 + y2 = 173x2 - 2y2 = -6
A. (2, -3) and (-2, 3) B. (2, 3), (2, -3), (-2, 3), (-2, -3) C. (1, 3) and (-1, -3) D. (1, 3), (1, -3), (-1, 3), (-1, -3)
Solve the problem.A plane flying a straight course observes a mountain at a bearing of 30.9° to the right of its course. At that time the plane is 
from the mountain. A short time later, the bearing to the mountain becomes 40.9°. How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a km)?
A. 10.2 km B. 11.5 km C. 4.2 km D. 6.3 km
Use a proportion to solve the problem.On a map of the Thunderbird Country Club golf course, 2.5 inches represent 30 yards. How long is the 16th hole if the map shows 13.5 inches?
A. 405 yards B. 5.6 yards C. 1012.5 yards D. 162 yards