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Question Number 120839 by bramlexs22 last updated on 03/Nov/20

Answered by mindispower last updated on 03/Nov/20

$$x\in \mathbb{Z}-\left\{1\right\}$$$$\Rightarrow \underset{k=2}{\sum ^{x-1}}\frac{x-k}{x-1}=5$$$$\Rightarrow \left(\frac{x-2+1}{x-1}\right)\left(\frac{x-2}{2}\right)=5$$$$\Rightarrow 10(x-1)=(x-2)(x-1)=0$$$$\iff (x-1)(10-x+2)=0\Rightarrow (12-x)(x-1)=0$$$$\Rightarrow x=12,sincex\ne 1$$

Commented by bramlexs22 last updated on 03/Nov/20

$$\mathrm{thank}\mathrm{you}$$

Answered by talminator2856791 last updated on 03/Nov/20

$$\underset{k=1}{\sum ^{x-2}}\frac{k}{x-1}=5$$$$\underset{k=1}{\sum ^{x-2}}k=5x-5$$$$\frac{(x-2)(x-1)}{2}=5x-5$$$$x^2-3x+2=10x-10$$$$x^2-13x+12=0$$$$(x-12)(x-1)=0$$$$x=12$$$$-----$$$$\mathrm{answer}:d$$

Answered by TANMAY PANACEA last updated on 03/Nov/20

$$a=x-2$$$$d=-1$$$$T_n=a+(n-1)d$$$$1=(x-2)+(n-1)\times -1$$$$1=(x-2)-n+1$$$$n=x-2$$$$LHS$$$$\frac{(x-2)+(x-3)+(x-4)+...+1}{x-1}$$$$\frac{x-2}{2}[x-2+1]\times \frac{1}{x-1}\to \frac{n}{2}(a+l)$$$$=\frac{x-2}{2}$$$$\frac{x-2}{2}=5$$$$x=12$$

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