calculate-lim-x-0-1-x-x-2-x-n-1-x-n-2-

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

c a l c u l a t e {l i m}_{x \to 0} \frac{\sqrt{1 + x + x^{2} + \dots . + x^{n}} - 1}{x^{\frac{n}{2}}}

Answered by jagoll last updated on 19/Jan/20

\lim_{x \to 0} \frac{(1 + x + x^{2} + x^{3} + \dots + x^{n}) - 1}{(\sqrt{1 + x + x^{2} + \dots + x^{n}} + 1) x^{\frac{n}{2}}} =

\lim_{x \to 0} \frac{x^{1 - \frac{n}{2}} + x^{2 - \frac{n}{2}} + x^{3 - \frac{n}{2}} + \dots + x^{\frac{n}{2}}}{(2)} = 0

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