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If-1-1-3-2-2n-1-n-a-n-1-b-1-2-n-1-c-for-a-b-c-integers-number-find-2a-b-3c-




Question Number 212496 by efronzo1 last updated on 15/Oct/24
 If 1.1!+3.2!+...+(2nāˆ’1).n!    = a.(n+1)!+b(1!+2!+...+(n+1)!)+c    for a,b,c integers number   find 2aāˆ’b+3c
$$\:\mathrm{If}\:\mathrm{1}.\mathrm{1}!+\mathrm{3}.\mathrm{2}!+…+\left(\mathrm{2n}āˆ’\mathrm{1}\right).\mathrm{n}!\: \\ $$$$\:=\:\mathrm{a}.\left(\mathrm{n}+\mathrm{1}\right)!+\mathrm{b}\left(\mathrm{1}!+\mathrm{2}!+…+\left(\mathrm{n}+\mathrm{1}\right)!\right)+\mathrm{c}\: \\ $$$$\:\mathrm{for}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{integers}\:\mathrm{number} \\ $$$$\:\mathrm{find}\:\mathrm{2a}āˆ’\mathrm{b}+\mathrm{3c}\: \\ $$

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