what is 1+2+3+4+5+6 all the way up to 100?

Question

answers will be given next week

Answer 1

Notice that 0+100=100, 1+99=100, 2+98=100, ...
And you have 50 lots of them (0 up to 49 paired); so 50*100=5000. Then you add the middle 50 to it:

5050


Extra info:
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Gauss was asked this question by his teacher when in primary school (the teacher wanting to keep him occupied for a while); Gauss gave the answer almost immediately -- and it is believed that he used this very method to do it.

But as has been mentioned below -- there are general equations to find the sum of series up to the nth term:

S = n(a+l)/2
S = n(2a+(n-1)d)/2

Answer 2

Member since: March 18, 2007
Total points: 257 (Level 2)
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--%Best answer

ozo
0



Notice that 0+100=100, 1+99=100, 2+98=100, ...
And you have 50 lots of them (0 up to 49 paired); so 50*100=5000. Then you add the middle 50 to it:

5050

Answer 3

This the sum of the first 100 terms of the arithmetic progression that starts at 1 and has constant r =1. We know that the sum of the first n terms of an arithmetic progression that starts at a_1 and has constant r is given by S(n) = ((a_1 + a_n)n) /2.

In our case , it's kinda simple, we have a_1 =1 , n =100, a_n =100 and r =1. Therefore, our sum is S(n) = ((n+1)n)/2. Letting n =100, we get S(100) = (101 . 100)/2 = 5050

Answer 4

There is a formula to calculate questions like this, which is:
Number of terms(1st term + last term)/ 2.

So the answer to this question is:

101(1+100)/2= 5050

Answer 5

to add any numbers [n(n+1)]/2 is used where n is the last digit till u want the sum.
Here, n=100 so by substituting in above formula,
we get-----=[100*(100+1)]/2
=5050
u can check it!!

Answer 6

Sum = (100/2)[1+100) = 5050

Formula used is
Sn = (n/2)(a+l)

Answer 7

it is a serie form of

n(n+1)/2 = 100(100+1)/2 = 5050

Answer 8

i agree with ozo and that is the answer i would have given to you myself pick one from each side they will give you hundred
then multiply by 50
100 * 50 =5000 +50 = 5050

Answer 9

(100+1) + (99+2) +....(51+50)
(101) + (101) + ... (101)
101 X 50
= 5050