IES Math Club

For an example....
If I asked you to add all the numbers between one and one hundred, you will stay for hours adding every number with the others, but if you added 1 and 100 this will add up to 101, and if you add 2 and 99 it will also add to 101, 3 and 98 are the same.
So you’ll add 101 for 49 times and the last remaining time will be 50+51 and there will not be a middle number because the number of terms you want to add is an even number, so that will make it 101 for 50 times.
So instead of adding all the numbers between 1 and 100 you’ll just multiply 101 by 50 and the answer will be 5050.
(As in example 1)
But what if it’s an odd number? Like adding all the numbers from zero to one hundred
that will make the algorithm different because you will add an odd number of terms which is
101 terms
If you tried to make the same algorithm of adding the first and the last terms together, you
will add 0+100 and that will add up to 100, 1+99 and that will also add up to 100 , 2+98 and
so on...but there will be a middle number this time and that is 50, so you will add 100 for
fifty times and there will be the number 50 with no opposite term to add... so you will add it
after you finish your multiplication (as in example 2)
The summation has so many uses such as:
• Some calculations that are made by statisticians
• Calculating Euler’s number
• Used in the binomial theorem for integer positive power