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Q.

Sum of all-natural numbers from 1 to 100 _____.


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a

5050

b

50

c

4550

d

5150 

answer is A.

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Detailed Solution

We are asked to find the sum of all natural numbers from 1 to 100
We know that the series of natural numbers is
1, 2, 3, 4, ……, 100
Here, we can see that it forms an A.P
We know that the natural numbers are in A.P with first term 1 and last term as 100
We know that the sum of n terms of the A.P is given as
S n = n 2 a+ a n  
Where a n   is the last term of the series.
By using the above formula to natural numbers from 1 to 100 then we get
⇒ S 100 = 100 2 (1+100) ⇒ S 100 =50×101 ⇒ S 100 =5050  
Therefore we can conclude that the sum of natural numbers from 1 to 100 is 5050
 
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