1 page

1 page is torn from the book. The sum of the page numbers of all the remaining pages is 15,000. What numbers did the pages have on the page that was torn from the book?

Correct result:

x₁ =  112
x₂ =  113

Solution:

$$\begin{gathered} {\displaystyle \frac{1}{2}}\cdot n(n+1)=15000+x \\ n\cdot (n+1)=30000+2x \\ o=\sqrt{30000}=100\sqrt{3}\doteq 173.2051 \\ n\cdot (n+1)=173\cdot 174 \\ n=174 \\ x={\displaystyle \frac{1}{2}}\cdot n\cdot (n+1)-15000={\displaystyle \frac{1}{2}}\cdot 174\cdot (174+1)-15000=225 \\ x=x_1+x_2 \\ {x}_1=x\mathrm{/}2-0.5=225\mathrm{/}2-0.5=112 \end{gathered}$$

$$\begin{gathered} x_2=x_1+1=112+1=113 \\ \text{ Verifying Solution: } \\ s={\displaystyle \frac{n}{2}}\cdot (1+n)={\displaystyle \frac{174}{2}}\cdot (1+174)=15225 \\ {s}_2=s-x_1-x_2=15225-112-113=15000 \end{gathered}$$

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