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Question Number 29196 by mathshooter last updated on 05/Feb/18

$$\mathrm{Let}\mathrm{s}={\mathrm{n}}_{{\mathrm{c}}_1}-(1+\frac{1}{2}){\mathrm{n}}_{{\mathrm{c}}_2}+(1+\frac{1}{2}+\frac{1}{3}){\mathrm{n}}_{{\mathrm{c}}_3}$$$$+.......+{(-1)}^{\mathrm{n}-1}(1+\frac{1}{2}+\frac{1}{3}+....+\frac{1}{\mathrm{n}}){\mathrm{n}}_{{\mathrm{c}}_{\mathrm{n}}}$$$$\mathrm{then}\mathrm{prove}\mathrm{that}\mathrm{s}\times \mathrm{n}=1.$$

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