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Question Number 78623 by mathmax by abdo last updated on 19/Jan/20

$$calculate{lim}_{x\to 0}\frac{\sqrt{1+x+x^2+....+x^n}-1}{x^{\frac{n}{2}}}$$

Answered by jagoll last updated on 19/Jan/20

$$\underset{x\to 0}{\lim }\frac{(1+\mathrm{x}+{\mathrm{x}}^2+{\mathrm{x}}^3+...+{\mathrm{x}}^{\mathrm{n}})-1}{(\sqrt{1+\mathrm{x}+{\mathrm{x}}^2+...+{\mathrm{x}}^{\mathrm{n}}}+1){\mathrm{x}}^{\frac{\mathrm{n}}{2}}}=$$$$\underset{x\to 0}{\lim }\frac{{\mathrm{x}}^{1-\frac{\mathrm{n}}{2}}+{\mathrm{x}}^{2-\frac{\mathrm{n}}{2}}+{\mathrm{x}}^{3-\frac{\mathrm{n}}{2}}+...+{\mathrm{x}}^{\frac{\mathrm{n}}{2}}}{\left(2\right)}=0$$$$$$

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