Find the sum of the first one hundred positive integers. see fig 6.26
1 answer:
Here's a pattern to consider:
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.
1+100=101
2+99=101
3+98=101
4+97=101
5+96=101
.....
This question relates to the discovery of Gauss, a mathematician. He found out that if you split 100 from 1-50 and 51-100, you could add them from each end to get a sum of 101. As there are 50 sets of addition, then the total is 50×101=5050
So, the sum of the first 100 positive integers is 5050.
Quick note
We can use a formula to find out the sum of an arithmetic series:
Where s is the sum of the series and n is the number of terms in the series. It works for the above problem.
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<h2>Answer explanation:</h2>
If a coin is fair then it has two faces , one is heads and the another is tails.
The probability getting any favorable outcomes is given by the formula :-
So the factor effecting probability is just the number of favorable outcomes and total outcomes.
If a coin is tossed then the probability of getting heads will be :-
To get heads always this should be 1 , which can be happen if number of favorable outcomes is equal to total outcomes.
i.e. Number of heads = Number of total outcomes, this means coin should be biased.
Catching the coin in mid-air can never be a factor for this.
Therefore, the little brother's theory is false.
Answer:
Step-by-step explanation:
The given fraction is:
We need to solve it.
The LCM of 168 and 180 is 2520.
So,
So, the required answer is equal to .