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關(guān)于前段時(shí)間所謂“韋神”出的“難題”

2023-04-01 12:20 作者:げいしも_蕓 0人讀過(guò) | 我要投稿

先看題

我們直接開(kāi)始解答

$%5Cprod_%7B1%5Cleq%20i%2Cj%5Cleq%20n%7D%5Cfrac%7B1%2Ba_ia_j%7D%7B1-a_ia_j%7D%5Cgeq1%5CLeftrightarrow%5Csum_%7B1%5Cleq%20i%2Cj%5Cleq%20n%7D%5B%5Cln(1%2Ba_ia_j)-%5Cln(1-a_ia_j)%5D%5Cgeq%200$

而

$%5Csum_%7B1%5Cleq%20i%2Cj%5Cleq%20n%7D%5B%5Cln(1%2Ba_ia_j)-%5Cln(1-a_ia_j)%5D$

$%3D%5Csum_%7B1%5Cleq%20i%2Cj%5Cleq%20n%7D%5Cleft%20(%5Csum_%7Bk_1%3D1%7D%5E%7B%2B%5Cinfty%7D(-1)%5E%7Bk_1%2B1%7D%5Cfrac%7B(a_ia_j)%5E%7B2k_1%2B1%7D%7D%7B2k_1%2B1%7D%2B%5Csum_%7Bk_2%3D1%7D%5E%7B%2B%5Cinfty%7D(-1)%5E%7Bk_2%2B1%7D%5Cfrac%7B(-a_ia_j)%5E%7B2k_2%2B1%7D%7D%7B2k_2%2B1%7D%5Cright)$

$%3D2%5Csum_%7Bk%3D0%7D%5E%7B%2B%5Cinfty%7D%5Csum_%7B1%5Cleq%20i%2Cj%5Cleq%20n%7D%5Cfrac%7B(a_ia_j)%5E%7B2k%2B1%7D%7D%7B2k%2B1%7D$

$%3D%5Csum_%7Bk%3D0%7D%5E%7B%2B%5Cinfty%7D%5Cleft(%5Cfrac%7B2%7D%7B2k%2B1%7D%5Csum_%7Bi%3D1%7D%5Ena_i%5E%7B2k%2B1%7D%5Csum_%7Bj%3D1%7D%5Ena_j%5E%7B2k%2B1%7D%5Cright)$