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...
Use a day counting table to find the exact number of days from the first date to the second date. Assume the year is not a leap year unless otherwise indicated.January 15 to July 31 (a leap year)
A. 197 B. 196 C. 213 D. 198
Find the domain of the variable in the equation. Write the answer in interval notation.
= 
A. (-?, -4) ? (8, ?) B. (-?, 4) ? (4, 8) ? (8, ?) C. (-?, -4) ? (-4, 8) ? (8, ?) D. (-4, 8) ? (8, ?)
Perform the indicated operation and, if possible, simplify.
÷ 
A. 
B. 
C. 
D. 
A function and its first and second derivatives are given. Use these to find any points of inflection. Round your answers to two decimal places.
?
A. 
B. 
C. 
D. 
E. no points of inflection