What is the sum of:
1+2+3+4+5+......+100???
Sum of first hundred natural numbers?
2008-12-15 2:40 pm
回答 (5)
2008-12-15 2:43 pm
✔ 最佳答案
The sum of the first n natural numbers is given by Gauss' formula:n(n + 1)/2.
Here, n = 100, so the sum is
100*101/2 = 5050.
2008-12-15 11:23 pm
you can do the following:
0+100=100
1+99=100
2+98=100
3+97=100
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49+51=100
so, the sum is 50*100+50=5050
0+100=100
1+99=100
2+98=100
3+97=100
.
.
.
.
49+51=100
so, the sum is 50*100+50=5050
2008-12-15 10:51 pm
We have a formula to count first n natural numbers as
n(n-1)/2
Here n=100
so
sum is
100(100-1)/2=100(99)/2
=9900/2=4950
n(n-1)/2
Here n=100
so
sum is
100(100-1)/2=100(99)/2
=9900/2=4950
2008-12-15 10:49 pm
Gauss did it when he was 6 years old.
Sum=n/2(1st + last)=50(101)=5050
Sum=n/2(1st + last)=50(101)=5050
2008-12-15 10:45 pm
(total terms)(first term + last term)/2
1 + 2 + 3 + 4 + 5 + ...... + 100
= 100(1 + 100)/2
= 100(101)/2
= 10100/2
= 5050
1 + 2 + 3 + 4 + 5 + ...... + 100
= 100(1 + 100)/2
= 100(101)/2
= 10100/2
= 5050
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