Arithmetic of series

steven187

hello all

a simple question how come

$$\sum_{k=1}^{n} k- \sum_{k=1}^{n} (k-1) \not= 1$$

even though i know if you expand it out you would get n, isnt there an arithmetic property of series that relates to this?

thanxs

whozum

The sum of the consecutive sequence of integers starting with 1 is

$$\frac{1}{2}n(n+1)$$ where n is the last (and largest) member of the sequence.

so from here we can see that the set of any consecutive set of integers has the sum given by

$$\frac{1}{2}n_1(n_1+1) - \frac{1}{2}n_2(n_2+1)$$, combining:

$$\frac{1}{2}(n_1^2 + n_1 - n_2^2 - n_2)$$

steven187

hello there

thanxs for that, i should have remembered something simple like that

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving