Question 46

Evaluate $$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...... $$?

Solution

$$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...... $$

Use GP formula as

$$\frac{(1-r^n)}{(1-r)}$$

here $$n = \infty$$

therefore, $$\left(\frac{1 - \left(\frac{1}{2}\right)^{\infty}}{1 - \left(\frac{1}{2}\right)}\right)$$

$$\frac{1}{\left(\frac{1}{2}\right)} = 2$$

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