First slide

Introduction to limits

Question

If $| x | < 1,$ then $\underset{n \to \infty}{l i m} (1 + x) (1 + x^{2}) (1 + x^{4}) ....... (1 + x^{2 n}) =$

Moderate

A

$\frac{1}{x}$
B

$\frac{1}{1 + x}$
C

$\frac{1}{1 - x}$
D

$\frac{1}{x - 1}$

Solution

$\lim_{x \to \infty} 1 + x + x^{2} + ..... + x^{2 n} = \frac{1}{1 - x}$

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