First, the calculation method is as follows:

1、 1+2+3+4+5+6+7+8+9+ 10=( 1+9)+(2+8)+(3+7)+(4+6)+5+ 10=55。

2. Let the sequence {an}(n is the subscript), a 1= 1, d= 1(d is the tolerance), n= 10, sn = n * a1+n * (n

Second, the method introduction:

1, find the law, easy to calculate.

2. Use the series summation formula (see 2 above).

3. Write code and input and output results.

Third, the historical source of mathematics:

1, the systematic learning of sequence can be traced back to the limit thought: when using the limit thought to solve the problem of irregular area, the sum of sequence is naturally derived, which makes the systematic learning of sequence sum necessary. Because I can't sum without a series, the most basic sum at that time was the sum of squares of natural numbers, which can be traced back to Archimedes' "exhaustive method".

2. When Leibniz founded calculus, he thought of a structure. The original material of this structure still comes from Pascal table. Through Pascal table, Leibniz's thought makes it possible to sum any sequence. Finally, through the introduction of limit thought, this thought was realized, Leibniz got a series of profound results, and the basic formula of calculus appeared.

3. For the understanding of function structure, Fourier took a step further and established Fourier series, which laid the foundation for the unified series of projection decomposition of function space in the future. At this time, the summation of series is defined as series and becomes a tool of mathematics, rather than the simplest calculation of demand. This is how pure mathematics developed.