Question

1 + 1⁄2 + 1⁄4 + 1⁄8 + 1⁄16 + 1⁄32 + 1⁄64. . . Notice that the denominator of each fraction in the sum is twice the denominator that comes before it. If you continue adding on fractions according to this pattern, when will you reach a sum of 2?

Answer 1

$a_1=1\\ q=\dfrac{1}{2}$

$|q|$ therefore, the sum of this infinite geometric series can be calculated using the formula $S=\dfrac{a}{1-q}$.

So, $S=\dfrac{1}{1-\dfrac{1}{2}}=\dfrac{1}{\dfrac{1}{2}}=2$

If 2 is the sum of this infinite series, then you'll never reach it.