Question 109
Find the value of expression.
$$8\left(1 + \frac{1}{2} + \frac{1}{4}.....\infty\right)$$
Solution
$$8\left(1 + \frac{1}{2} + \frac{1}{4}.....\infty\right)$$ is an infinite GP (the expression under the brackets) with the first term being 1, and the common ratio being $$\frac{\ 1}{2}$$or 0.5.
For infinite GP with common ratio less than 1, the sum is $$\ \frac{\ a}{(1-r)}$$
Applying the same in this, we get the sum as $$\ \frac{\ 1}{(1-0.5)}$$, which is 2.
Hence, the value of the entire expression is $$8\times2$$, which is 16.
