Question

1
limx→1(1+x+x2+……...+xm−1)
= …….
1
m-1
m
-1

Answer 1

Answer on Question #52165 – Math - Calculus

$$\lim_{x \to 1} 1 + x + x^{2} + \cdots + x^{m-1}$$

a) 1

b) m-1

c) m

d) -1

Solution

$$\lim_{x \to 1} (1 + x + x^{2} + \cdots + x^{m-1}) = \lim_{x \to 1} \left( \sum_{i=0}^{m-1} x^{i} \right) = \sum_{i=0}^{m-1} \left( \lim_{x \to 1} (x^{i}) \right) = \sum_{i=0}^{m-1} 1^{i} = \sum_{i=0}^{m-1} 1 = \mathbf{m}$$

Answer: c) m.

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