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Question Number 162926 by qaz last updated on 02/Jan/22

$$\underset{\mathrm{x}\to 0}{\lim }\frac{1}{{\mathrm{x}}^{\mathrm{n}+1}}[{(1+\mathrm{x}+\frac{\mathrm{x}}{2}+...+\frac{{\mathrm{x}}^{\mathrm{n}}}{\mathrm{n}})}^{\frac{1}{\mathrm{x}+\frac{\mathrm{x}}{2}+...+\frac{{\mathrm{x}}^{\mathrm{n}}}{\mathrm{n}}}}-{(1+\mathrm{x}+\frac{\mathrm{x}}{2}+...+\frac{{\mathrm{x}}^{\mathrm{n}+1}}{\mathrm{n}+1})}^{\frac{1}{\mathrm{x}+\frac{\mathrm{x}}{2}+...+\frac{{\mathrm{x}}^{\mathrm{n}+1}}{\mathrm{n}+1}}}]=?$$

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