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zalisa [80]
3 years ago
5

Which example proves the following

Mathematics
1 answer:
worty [1.4K]3 years ago
8 0

Answer:

The prime number 2.

Step-by-step explanation:

<em>Odd number + Odd number = Even number</em>

An odd number plus another odd number equals an even number. And most prime numbers are odd, so you might think this is true. Is it?

Wrong. The prime number 2 is an even number and

<em>Even number + Odd number = Odd number</em>

<em>Odd number + Even number = Odd number</em>

<em />

So, there is a number that can make the sum of two prime numbers odd.

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In the geometric progression 1, 2, 4… what term is 512?
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The next term is double the previous term, so that the n-th term is given recursively by

\begin{cases}a_1=1\\a_n=2a_{n-1}&\text{for }n>1\end{cases}

This rule tells us that

a_2=2a_1

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a_4=2a_3=2^3a_1

and so on, with the explicit rule

a_n=2^{n-1}a_1=2^{n-1}

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If 512 is the k-th term in the sequence, then

512=2^{k-1}\implies\log_2512=\log_22^9=\log_22^{k-1}\implies9=k-1\implies k=10

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