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its 5035

the summarian notation tells you that

(sum of all #from 0 to a number'N'

(sum of all #from 0 to N) = (n)+(n-1)+(n-2)+(n-3)+...+(2) +(1) or

(sum of all #from 0 to N) = (1)+ (2) + (3) + (4)+...+(n-1)+(n)

the two different sums are aligned by columns. now add the two colunms accordingly and you'll get

2x(sum of all #from 0 to N)=(n+1)+(n+1)+...+(n+1) (n+1)is added n times

so

2x(sum of all #from 0 to N) =n(n+1)

(sum of all #from 0 to N) =n(n+1)/2

so (sum of 5 to 100) = (sum of 0 to 100)- (sum of 0 to 5)

=100(101)/2 - 5(6)/2 = 5050 - 15 = 5035

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Q: What is the sum of the whole numbers from 5 up to 100?
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How many whole numbers are there upto 100?

Depending on how you look at it, there are either 99 or 100 whole numbers up to 100. If you mean up to and including 100, then the answer is 100 whole numbers, if not, then the answer is 99 whole numbers.


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It is instructive to note that you can rewrite 1+2+3+4....+99+100 as 1+100+2+99+3+98....+50+51 Then you can group each pair of numbers as (1+100)+(2+99)+(3+98)+...+(50+51) All of these couplets add up to 101, and there are 50 of them. Thus the sum of the first 100 whole numbers is 50x101. This can be calculated at 5,050.


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