Question

what is the sum of all natural numbers from 1to100?

Answer 1

Hii There!!!

We know that sum of 'n' natural numbers is given by : n ( n + 1 ) /2

So, sum of 'n' natural numbers from 1 to 100

=> 100( 100 + 1 )/2

=> 100 (101) /2

=> 5050

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Answer 2

1 + 2 + 3 + 4 + … + 98 + 99 + 100

I noticed that if he was to split the numbers into two groups
Like (1 to 50 and 51 to 100)
I could add them together vertically to get a sum of 101.
1 + 2 + 3 + 4 + 5 + … + 48 + 49 + 50

100 + 99 + 98 + 97 + 96 + … + 53 + 52 + 51

1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
.
.
.
48 + 53 = 101
49 + 52 = 101
50 + 51 = 101

I realized then that his final total would be 50(101) = 5050.

The sequence of numbers (1, 2, 3, … , 100) is arithmetic and when we are looking for the sum of a sequence, we call it a series. Thanks to Gauss, there is a special formula we can use to find the sum of a series:
S=n(n+1)/2
S is the sum of the series and n is the number of terms in the series, in this case, 100.
S=100(100+1)/2
ans is 5050
Hope this helps!
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