TW Mathemeticians

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Stuttrboy

Veteran X
Is there a way to calculate the sum of a series of numbers? Like 1 thru 1000 or would I have to actually calculate them all out individually? 1+2+3+4...+999+1000.

Anyone know a shorter way to do this?
 
What grade are you in?
additional equation u might want since def posted it already*
geometric_sequence_18.gif
 
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Imagine there are 1001 people at a party. Everyone is going to shake hands with everyone else once and we're going to count the number of handshakes. The first person goes round and does 1000 (they don't shake their own hands), the second person does 999 handshakes (they've already shaken hands with the first person), then the next does 998 etc. so the total number of handshakes is 1+2+3+4...+999+1000.

On the other hand, the number of handshakes is the number of ways we can choose two people (order doesn't matter) out of 1001. There are 1001 choices for the first person, 1000 for the second and we must divide by two as the order doesn't matter. Hence there are 1001*1000/2.

Another way you could see this is by pairing up the numbers as
(1000 + 1) + (999 + 2) + (998 + 3) + ... = 1001 + 1001 + ...

A third way would be to note that if you imagine these as 1x1 blocks and arrange them as in the sum and work out the area, after some cutting up and reassembling it's the area of a triangle with height (n+1) and base n. I'm too lazy to draw pictures.

Hence, in general 1 + 2 + ... + n = n(n+1)/2

P.S. kMz.: it's not a geometric series.
 
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