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Category: Algebra

1-2-2-3-3-4-4-5-17-18-

Question Number 10493 by ABD last updated on 14/Feb/17 12!+23!+34!+45!++1718!=? Answered by mrW1 last updated on 14/Feb/17 sincen(n+1)!=1n!1(n+1)!12!+23!+34!+45!++1718!$$=\left(\frac{\mathrm{1}}{\mathrm{1}!}−\frac{\mathrm{1}}{\mathrm{2}!}\right)+\left(\frac{\mathrm{1}}{\mathrm{2}!}−\frac{\mathrm{1}}{\mathrm{3}!}\right)+\left(\frac{\mathrm{1}}{\mathrm{3}!}−\frac{\mathrm{1}}{\mathrm{4}!}\right)+\centerdot\centerdot\centerdot+\left(\frac{\mathrm{1}}{\mathrm{17}!}−\frac{\mathrm{1}}{\mathrm{18}!}\right) \