# Thread: 199 and Counting

1. ## 199 and Counting

Group the counting numbers as follows: (1), (2,3), (4,5,6), (7,8,9,10), (11,12,13,14,15), ... Notice that the first group has one number, the second group has two numbers, etc. The 199th group would have 199 numbers. What is the sum of the numbers in the 199th group? <img src=/S/munch.gif border=0 alt=munch width=19 height=17>

2. ## Re: 199 and Counting

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">3940399</span hide>

3. ## Re: 199 and Counting

Okay - On this one, I'd like to see your method. <img src=/S/read.gif border=0 alt=read width=19 height=33>

4. ## Re: 199 and Counting

<span style="background-color: #FFFF00; color: #FFFF00; font-weight: bold">I use the well-known formula n*(n+1)/2 for the sum of the numbers 1 ... n.
The 198th group of numbers ends at the number 198*199/2 = 19701. The sum of *all* numbers up to and including 19701 is 19701*19702/2 = 194074551.
The 199th group of numbers ends at the number 199*200/2 = 19900. The sum of *all* numbers up to and including 19900 is 19900*19901/2 = 198014950.
So the sum of the numbers in the 199th group is 198014950-194074551 = 3940399.</span hide>

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