Find all natural number values for n for which the given statement is false.
-$$2 ^ { n } 2 n + 2$$
A) $n = 1,2$, or 3
B) $n = 1$ or 2
C) $\mathrm { n } = 1,2$, or 4
D) $n 3$

Question

Find all natural number values for n for which the given statement is false.
-$$2 ^ { n } > 2 n + 2$$
A) $n = 1,2$, or 3
B) $n = 1$ or 2
C) $\mathrm { n } = 1,2$, or 4
D) $n > 3$

Quizplus · Accepted Answer

For $n = 1$, $2^1 = 2$ which is not greater than $2(1) + 2 = 4$, making the statement false. For $n = 2$, $2^2 = 4$ which is not greater than $2(2) + 2 = 6$, making the statement false. For $n = 3$, $2^3 = 8$ which is not greater than $2(3) + 2 = 8$, making the statement false. For $n = 4$ and onwards, $2^n$ grows faster than $2n + 2$, making the statement true. Therefore, the statement is false for $n = 1, 2,$ and $3$.

Find All Natural Number Values for N for Which the Given