Prove that, for integer values of n such that 0 ≤ n 3^n$

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Prove that, for integer values of n such that 0 ≤ n < 4 $2^{n+2} > 3^n$ - AQA - A-Level Maths Pure - Question 5 - 2020 - Paper 1

Question 5

$Prove-that,-for-integer-values-of-n-such-that-0-≤-n-<-4--$2^{n+2}->-3^n$-AQA-A-Level Maths Pure-Question 5-2020-Paper 1.png$

Prove that, for integer values of n such that 0 ≤ n < 4 $2^{n+2} > 3^n$

Step 1

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Answer

For n = 0:

$2^{0+2} = 2^2 = 4$
$3^0 = 1$
So, $4 > 1$ is true.

Step 2

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Answer

For n = 1:

$2^{1+2} = 2^3 = 8$
$3^1 = 3$
So, $8 > 3$ is true.

Step 3

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Answer

For n = 2:

$2^{2+2} = 2^4 = 16$
$3^2 = 9$
So, $16 > 9$ is true.

Step 4

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Answer

For n = 3:

$2^{3+2} = 2^5 = 32$
$3^3 = 27$
So, $32 > 27$ is true.

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