Question

how to ad from 1 to 100

Answer 1

Just use the formula
Sn=n/2(2a+(n-1)d)
Given n=100
a =1
d =1
Sn= 100/2(2x1+(100-1)1)
Sn=50x101
Sn=5050
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Answer 2

8Here is your answer !!

____________________________

According to Carl's Gause method !!

No. in increasing order :

1 2. 3. 4. 5. 6. ...............100

No. in decreasing order :

100. 99. 98. 97. 96. ............. 1

Now add it , we get

101. 101. 101. 101. ..................101

This sums occurs 100s time , therefore multiply it by 100 we get

100 x 101 = 10100

In this 1 to 100 counted two times therefore, half of this is

10100/2 = 5050 and this is answer !

So, according to this theory a simple formula were discovered to find the sum of any number s and that is,

Sn = n/2[2a + (n-1)d]

We have ,
1,2,3,4.......100

Here,

a = 1
d = 1
n = 100


Put the given values

S₁₀₀ = 100/2[ 2 x 1(100-1)1]

S₁₀₀ = 50 x 101

∴ S₁₀₀ = 5050

∴ The sum of all numbers from 1 to 100 is 5050 .


Thanks !!