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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Expand and simplify the given expression by use of Pascal's triangle.
3
A. 
x6 + 
x3 + 64
B. 
x3 + 
x2 + 16x + 64
C. 
x3 + 
x2 + 64
D. 
x3 + 
x2 + 16x + 64
Add or subtract, if possible. Assume that all variables represent non-negative values. Simplify your answer. 
- 
A. -7
B. 9x
C. -7x
D. -7x
The following sentence involves decimals. Write the decimal in words.One ton is equal to 907.18 kilograms.
A. Nine hundred seventy and eighteen hundredths B. Nine hundred seventy and eighteen thousandths C. Nine hundred seven and eighteen hundredths D. Nine hundred seven and eighteen thousandths
Evaluate.i27 + i23
A. -2 B. -2i C. 0 D. 2