Question

what is sum of even natural number 1 to 100

Answer 1

Sum of all even numbers:

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

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



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

where, aa = First element in AP, ll = Last element in AP.

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

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

dd = difference between two consecutive elements.

So, here l=98,a=2,n=?l=98,a=2,n=?

For nn:

98=2+(n−1)298=2+(n−1)2

n−1=48n−1=48

n=49n=49

So, Sn=492[2+98]Sn=492[2+98]

Sn=2450

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

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.. Hope it is helpful ✌ ✌

Answer 2

there are 50 numbers
sum of even numbers=N/2(2a+(n-1)d)

here N=50
a=2,d=2
substitute these values
we get sum=2550


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