Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.
is divisible by 2
What will be an ideal response?
First, we show that the statement is true when n = 1.
For
This is a true statement and Condition I is satisfied.
Next, we assume the statement holds for some k. That is,
is divisible by 2 is true for some positive integer k.
We need to show that the statement holds for . That is, we need to show that
is divisible by 2.
So we assume is divisible by 2 and look at the expression for n = k + 1.
Since is divisible by 2, then
for some integer m. Hence,
Condition II is satisfied. As a result, the statement is true for all natural numbers n.
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Find the limit, if it exists.
A. Does not exist
B. -
C. 0
D.
Use the compound interest formulas A = Pnt and
to solve.Find the accumulated value of an investment of $1,900 at 8% compounded quarterly for 2 years.
A. $2,216.16 B. $2,226.15 C. $2,204.00 D. $1,976.76
Multiply.(x - 9)2
A. x + 81 B. x2 + 81 C. x2 - 18x + 81 D. 81x2 - 18x + 81
Perform the indicated operations and simplify. -
+
A.
B.
C.
D.