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...
Find the first term and the common ratio of the geometric sequence.an = -(1.06)n-1
A. a1 = 1.06, r = 0.06 B. a1 = -1, r = 1.06 C. a1 = -1, r = -1.06 D. a1 = 0, r = (1.06)n-1
Convert the units.417 mL = 
L
A. 417,000 L B. 0.417 L C. 4.17 L D. 41,700 L
Write fraction as decimal number. Use bar notation for repeating decimals.
A. 0.9
B. 0.93
C. 0.9375
D. 0.937
Solve the problem.The logistic growth function f(t) = 
describes the population of a species of butterflies 
after they are introduced to a non-threatening habitat. How many butterflies are expected in the habitat after 16 months?
A. 320 butterflies B. 5120 butterflies C. 480 butterflies D. 278 butterflies