zhy seniors out of the college entrance examination papers math topics
Face feeling very interesting topic to share
Super unscientific sequence of a summing 2 (so why not a science)
Given n, m, k;
求$\sum_{x_{1}=1}^{n}\sum_{x_{2}=1}^{x_{1}}\sum_{x_{3}=1}^{x_{2}}...\sum_{x_{m-1}=1}^{x_{m-2}}\sum_{x_{m}=1}^{x_{m-1}}\sum_{i=1}^{k}a_{i}x_{m}^{i}$
solution part 1
(Polynomial simplified into monomials and converted to a combination of problems)
先求$\sum_{x_{1}=1}^{n}\sum_{x_{2}=1}^{x_{1}}\sum_{x_{3}=1}^{x_{2}}...\sum_{x_{m-1}=1}^{x_{m-2}}\sum_{x_{m}=1}^{x_{m-1}}\sum_{i=1}^{k}1$
Found that can be converted to seek length m, the minimum value of 1-n is monotonically ascending series, initially n, i.e. the difference value assigned assignment (n-1) th difference to reduce the chance of 1, allowing the remaining, and the number of programs allowed to be 0.
The separator method, obtains the number of programs for $ C_ {n + m-1 } ^ {m} $