设 $\sed{a_k}_{k=1}^n$ 为等差数列, 则 $$\bex a_1+\cdots+a_n=\frac{n(a_1+a_n)}{2}. \eex$$ Ref. [Proof Without Words: Partial Sums of an Arithmetic Sequence, The College Mathematics Journal]. A visual proof that a partial sum of an arithmetic sequence equals the number of the terms times the average of the first and last term.

[再寄小读者之数学篇](2014-11-19 等差数列的部分和)