Question

find the sum of the even number between 0 and 100​

Answer 1

Answer:

1000

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Answer 2

Answer:

Sum of all even numbers:

The series which we want to add can be given as :

2,4,6,8,....,96,98.

Now, Such series are calculated using A.P. (Arithmetic Progressions)

Sum of N numbers in AP is given by Sn=n2[a+l]

where, a = First element in AP, l = Last element in AP.

According to the series we have number of total elements n which can be calculated as:

l=a+(n−1)d, where n = number of elements.

d = difference between two consecutive elements.

So, here l=98,a=2,n=?

For n :

98=2+(n−1)2

n−1=48

n=49

So, Sn=492[2+98]

Sn=2450

The sum of all even numbers between 1 to 100 (excluding 100) is : 2450

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