what is the sum of all natural numbers from one to hundred
Answers
Answer:
5050
Step-by-step explanation:
o calculate the sum of 1–100 there is a trick
First calculate the sum of 1–10
It is
1+2+3+4+5+6+7+8+9+10 = 55
Similarly the sum of next ten numbers, that is from 11–20
It is
11+12+13+14+15+16+17+18+19+20 = 155
From the above two sums it is clear that the sum of next ten numbers numbers would be 255.
Similarly we would get 355,455,555,655,755,855,955.
Now adding all these sums, that is
55+155+255+355+455+555+655+755+855+955 = 5050.
Edit- The above method is solved without any formulas. But there is a formula for solving this problem.
Sn=n(n+1)/2
The derivation of this formula-
Let Sn=1+2+3+.....+n (equation 1)
By rearrangement
Sn=n+(n−1)+(n−2)+....+1 (equation 2)
By adding equation 1 & 2
2Sn=(n+1)+(2+n−1)+(3+n−2)+.....+(n+1)
2Sn=(n+1)+(n+1)+(n+1)+....+(n+1)
In the above equation n+1 is added n times
Therefore,
2Sn=n(n+1)
Sn=n(n+1)/2
Here n=100
Sn=100∗101/2
=10100/2
=5050
Answer:
5050
Step-by-step explanation:
sum of all natural nos forms an AP
1,2,3,.....100
a=1,d=1. an=100
an=a+(n-1)d
100=1+(n-1)1
n=100
Sn=(n/2)[2a+(n-1)d]
=50(2+99(1))
=50*101
=5050