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Why is "for j = 1 to n" translate to this? Why is the upper bound always incremented by 1?

$$\sum_{j=1}^{n+1}1 $$

Why isn't it $$\sum_{j=1}^n1 $$

"for j = 1 to n" is written in pseudo code btw for algorithm analysis. Or is there a + 1 because of the final condition check when using summations to count the frequency count of for loops?

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It should be what you say it is. I'm not sure why you need to increment it by 1. Are you programming something, by any chance? –  Joe Z. Jan 2 '13 at 21:22
    
Can you provide the context? Where did you see this? Sometimes in programing 0 is the first number, which could cause the difference in notation. –  Calvin Lin Jan 2 '13 at 21:25
    
Saw it in a powerpoint, its written in pseudocode for algorithm analysis –  Code Crusader Jan 2 '13 at 21:27
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up vote 1 down vote accepted

I think you are backwards. In BASIC, For j=1 to N gives you N loops, with j=N in the final one. In Python, for j in (1,N) gives you N-1 loops, with j=N-1 in the final one. If you want N loops, you need to do for j in (1,N+1). What language are you working in?

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its written in pseudocode for algorithm analysis I'm thinking the + 1 is for the final condition check when using summations to count for loops? –  Code Crusader Jan 2 '13 at 21:31
    
@vincentbelkin: then I don't understand the +1 either. –  Ross Millikan Jan 2 '13 at 22:55
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To be precise, the Python "for" command loops over the given list and nothing else. It's just that the command "range(a,b)", which is often used to generate the list, produces the numbers $a \le i < b$. –  Hans Lundmark Jan 3 '13 at 8:37
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