Prove that the product of any two consecutive natural numbers is even.
1 answer:
Answer with Step-by-step explanation:
Let us assume the 2 consecutive natural numbers are 'n' and 'n+1'
Thus the product of the 2 numbers is given by
We know that the sum of 'n' consecutive natural numbers starting from 1 is
Thus from equation 'i' we can write
As we know that any number multiplied by 2 is even thus we conclude that the product of 2 consecutive numbers is even.
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Answer:
Step-by-step explanation:
We can use basic probability to find the probability that this roll is not a factor of 35.
First off, we know that with a six sided die there are 6 possible things we can roll.
1, 2, 3, 4, 5, or 6
Now, what are the factors of 35? The factors of 35 will be any whole number that can be multiplied by another whole number to get 35.
- We know
, so two factors are 1 and 35.
- We know
, so two factors are 5 and 7.
Therefore, the factors of 35 are 1, 5, 7, 35.
Both 5 and 7 are inside the range of 1-6. So the probability of rolling a side that's a factor of 35 will be since there are two factors and 6 possible options.
This means, logically, there is a chance of not rolling a factor of 35.
Hope this helped!