Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.Use the Principle of Mathematical Induction to show that the statement "5 is a factor of 7n - 2n" is true for all natural numbers. (Hint: 
What will be an ideal response?
When 
, so the statement is true when 
. Assume the statement is true for some natural number k. That is, 
for some integer m. Then,
.
So the statement is true for 
. Conditions I and II are satisfied; by the Principle of Mathematical Induction, the statement is true for all natural numbers.
You might also like to view...
Solve.Find the area of the kite shown. Round to the nearest hundredth, if necessary.
A. 776,630.00 in2 B. 1,553,260.00 in2 C. 194,157.50 in2 D. 388,315.00 in2
Use the fundamental identities to simplify the expression.sin2? + tan2? + cos2?
A. cos3? B. sin ? C. tan2? D. sec2?
Divide and simplify.
A. 40x4y2 + 16xy + 7
B. 5x4y2 + 2xy3 + 
C. 5x4y4 + 2x4y2 + 
D. 5x4y2 + 2xy + 
?
Refer to the figure above to find the length of segment 
.
?
A. 4 B. 3 C. 2 D. 7