Computing value of the series $S_N = \sum_{k=1}^{k=N} a_k$

Question

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Sum of n consecutive numbers

I am working on engineering problem where I have a series of the form:

$S_N = \sum_{k=1}^{k=N} a_k$

were $a_k = k$. I'm wondering, how do I compute the value of $S_N$ for $N=365$ and what type of series is this?

Answer 1

$S_N=a_1+a_2+a_3+\cdots+a_N$ where $a_k=k$

$\implies s_N=1+2+3+\cdots+N$ which is an arithmetic progression with $a=1$ and common difference $d=1$

$\implies s_N=\frac{N(N+1)}{2}$

see http://en.wikipedia.org/wiki/Arithmetic_progression#Sum