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.
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Solve the problem.The series ln(x) = (x - 1) - 
+ 
- . . . + (-1)n-1
can be used to estimate the value of ln(a) for any positive real number a such that 0 < a ? 2. Use the first five terms of this series to estimate 
Round to the nearest thousandth.
A. 1.717 B. -0.773 C. 1.047 D. 0.157
Use the theorem on bounds to establish the best integral bounds for the roots of the equation.2x3 - 3x2 - 4x + 4 = 0
A. -3 < x < 3 B. -1 < x < 3 C. -2 < x < 3 D. -3 < x < 2
Write the interval as an inequality involving x, and illustrate the inequality using the real number line.[-2, ?)
A. x ? -2
B. x > -2
C. x ? -2
D. x > -2
Use the order of operations to simplify the expression.(4 + 6)[4 + (4 + 4)]
A. 22 B. 18 C. 120 D. 48