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Question Number 115856 by bemath last updated on 29/Sep/20

$$Whichisgreater$$$$P=\left(1983\right)(1+2+3+...+1984),or$$$$Q=\left(1984\right)(1+2+3+...+1983)$$

Answered by bobhans last updated on 29/Sep/20

$$letz=1+2+3+4+...+1983$$$$nowconsiderP=\left(1983\right)(z+1984)$$$$P=1983z+1983\times 1984$$$$andQ=1984z$$$$checkP-Q=1983z+1983\times 1984-1984z=0$$$${it}^{\prime }strue.thereforethegreaterisP$$

Answered by floor(10²Eta[1]) last updated on 29/Sep/20

$$\mathrm{P}=1983.\left(\frac{1985.1984}{2}\right)=\frac{1983.1984.1985}{2}$$$$\mathrm{Q}=1984.\left(\frac{1984.1983}{2}\right)=\frac{1983.{1984}^2}{2}$$$$\mathrm{so}\mathrm{P}>\mathrm{Q}$$

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