Question-189127

Question Number 189127 by Mingma last updated on 12/Mar/23

Answered by Rasheed.Sindhi last updated on 12/Mar/23

((p!−(p−1)!)/((p−1)!))=2023 (((p−1)![p−1])/((p−1)!))=2023 p−1=2023 p=2024

$$\frac{{p}!−\left({p}−\mathrm{1}\right)!}{\left({p}−\mathrm{1}\right)!}=\mathrm{2023} \\ $$$$\frac{\left({p}−\mathrm{1}\right)!\left[{p}−\mathrm{1}\right]}{\left({p}−\mathrm{1}\right)!}=\mathrm{2023} \\ $$$${p}−\mathrm{1}=\mathrm{2023} \\ $$$${p}=\mathrm{2024} \\ $$

Commented by Mingma last updated on 13/Mar/23

Excellent!

Answered by Rasheed.Sindhi last updated on 13/Mar/23

((p!−(p−1)!)/((p−1)!))=2023 ((p!)/((p−1)!))−(((p−1)!)/((p−1)!))=2023 (((p−1)!×p)/((p−1)!))=2023+1 p=1024

$$\frac{{p}!−\left({p}−\mathrm{1}\right)!}{\left({p}−\mathrm{1}\right)!}=\mathrm{2023} \\ $$$$\frac{{p}!}{\left({p}−\mathrm{1}\right)!}−\frac{\cancel{\left({p}−\mathrm{1}\right)!}}{\cancel{\left({p}−\mathrm{1}\right)!}}=\mathrm{2023} \\ $$$$\frac{\cancel{\left({p}−\mathrm{1}\right)!}×{p}}{\cancel{\left({p}−\mathrm{1}\right)!}}=\mathrm{2023}+\mathrm{1} \\ $$$${p}=\mathrm{1024} \\ $$

Answered by Rasheed.Sindhi last updated on 13/Mar/23

((p!−(p−1)!)/((p−1)!))=2023 ((p!−(p−1)!)/((p−1)!))+1=2023+1 ((p!−(p−1)!+(p−1)!)/((p−1)!))=2024 (((p−1)!×p)/((p−1)!))=2024 p=2024

$$\frac{{p}!−\left({p}−\mathrm{1}\right)!}{\left({p}−\mathrm{1}\right)!}=\mathrm{2023} \\ $$$$\frac{{p}!−\left({p}−\mathrm{1}\right)!}{\left({p}−\mathrm{1}\right)!}+\mathrm{1}=\mathrm{2023}+\mathrm{1} \\ $$$$\frac{{p}!−\cancel{\left({p}−\mathrm{1}\right)!}+\cancel{\left({p}−\mathrm{1}\right)!}}{\left({p}−\mathrm{1}\right)!}=\mathrm{2024} \\ $$$$\frac{\left({p}−\mathrm{1}\right)!×{p}}{\left({p}−\mathrm{1}\right)!}=\mathrm{2024} \\ $$$${p}=\mathrm{2024} \\ $$

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