Imamdiallo18
06.09.2019 •
Mathematics
Prove that 9 divides 4" + 6n – 1 for n > 1 by mathematical induction.
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Ответ:
This is a classic problem I think that you mean
This problem clearly states to use proof by induction, follow the complete answer below.
Step-by-step explanation:
To prove something by induction we have to make a proposition first, in this case:
is divisible by 9
Where is the order of the proposition.
First we have to prove the first few orders, let's just check P(1):
which is clearly divisible by 9
Now let's assume that P(n) is true that means, our original proposition is true. Now let's try to find out whether P(n+1) is true:
The is divisible by 9 because we assumed that " is divisible by 9" was a true proposition. On the other hand has a factor of 9 regardless of n, thus is also divisible by 9 that means that P(n+1) is true and it follows that P(n) must also be true, thus proving our initial statement.
Ответ:
yes
Step-by-step explanation: